Let's talk about your goal
Historically, a "civilization" was defined in a one-world-centric and highly political way: if the ruling government, its supporters and military, were completely demolished — that civilization was considered destroyed. The Myans, the Easter Island peoples, Cahokia, the Olmec... Oh, for the most part their genetic code can be found lurking around today, but our history is littered with civilizations that once thrived and influenced our world — and yet are gone, leaving only ruins.
This is actually a good starting point for an answer. You want an entire species wiped out — but I posit that there's little to no difference between an entire species and an entire ethnic group. I watched during the 1990s as television brought horrific news about the Bosnian genocide. We're not talking about one empire destroying another — we're talking about peoples in Yugoslavia who had intermarried, done business with one another for decades (and generations), and yet (unbeknownst to the world) were harboring a hate that makes whatever nonsense is going on in the U.S. today look like a schoolroom spat. The result is known today as ethnic cleansing, which is simply a smaller scale of what you're looking for, "special cleansing* (See Merriam-Webster definition 3b).
Whether the ethnicity is wiped off the face of the Earth or the species is wiped off the face of the galaxy — it's the same thing. What's left behind are the memories of a once vibrant people.
Having got that out of the way... what can do this on a Grand Scale?
We're living through that right now and the experience is directly relatable. All you need is a disease that's impossible/ultra-hard to eradicate, that has a very long incubation period (to meet the needs of a non-FTL universe), and is 80%-90% mortality rate and you have a believable condition to wipe out a civilization — especially if your disease does something gratefully rare among human-encountered diseases: make the carrier impotent. Whomever survives the disease can't propagate the species. The civilization is dead in one generation upon every planet it touches.
However, in a non-FTL universe where light can always deliver a message faster than the disease can travel, it becomes less believable that this method would work to completely wipe out a civilization. Not impossible, but unlikely. You could use the excuse that the disease killed quickly to keep the knowledge from spreading ... but then comms would go dark. It wouldn't take long for someone in those million worlds to figure out that something was spreading (would make for a really cool story, though).
This one is so obvious it's a trope all to itself — but having just discussed the Bosnian Genocide it's a very real and very viable solution to your problem. L. Ron Hubbard used a basic concept to set the stage for Psychlo ownership of Earth (and every other planet they were awarded): they gassed the planet.1 If you have access to interplanetary resources, it's beyond conceivable that you can release enough poison into any atmosphere to bring down a civilization. Yes, there's always the possibility that someone is quick enough to get into their bunker and survive — but your universe has no FTL, which means its inhabitants are conditioned to thinking in terms of decades and centuries. Send a fleet of drones to gas a planet and keep it gassed for 100 years. Then send your colonists to take over the planet.2
To be fair, "war" could be described as the most viable delivery mechanism for whatever destroys the civilization (in which case it kinda doesn't belong on this list) because it could deliver the disease as easily as it could a poison gas. However, war is likely the only mechanism that can bring about complete destruction of a species: an intentional, focused pogrom that would survive the test of time to complete its task.
3. The collision of galaxies
A million planets without FTL travel means millions of years were used to achieve this marvelous pinnacle of civilization! But millions of years actually count in terms of astronomical events. That's enough time for galaxies to collide. While this could lead to a suspension-of-disbelief solution (you didn't restrict how short the destructive period had to be), it does run up against a fundamental axiom of good science fiction:
Space is big. Really big. You just won’t believe how vastly hugely mindbogglingly big it is. I mean you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space. (Douglas Adams, The Hitchhiker's Guide to the Galaxy)
Space is so big that it's conceivable for to galaxies to collide and not actually interrupt much of anything. Imagine the millions or billions of years required for the galaxies to actually collide and (let's say) pass through each other. "Whew!" some idiot might say, "that was a near miss!"
4. Something's wrong with the black hole...
If you need a natural phenomena that's not as slow as colliding galaxies but might not be as fast as war, consider something going wrong with the galaxy's central black hole. The easiest solution is an explosion. However, if you want ruins left behind for someone to find, this might not be the best solution.
As a conclusion, I'd like to return to the Bosnian Genocide. Yugoslavia had successfully repressed the hate for a while, but once it was allowed to resurface, it came back with a breath-taking mind-alteringly scary vengeance (if you, the reader, were not alive to experience the 90s... you really have no idea just how deep hate can run). And this is important.
I find a million-planet utopia unbelievable. Completely unbelievable. Unless, like Yugoslavia, it's suppressing the hate. It's nice to believe that humans can outgrow hate (and maybe someday we can), but I simply don't see it.3 But for the sake of your story, let's assume that for the time it took to get to a million planets your civilization was able to suppress all the hate...
5. Civil War
Nobody gives enough credit to the civilization-destroying capacity of civil war. Ancient civilizations were destroyed by it. Just because the U.S. survived its civil war doesn't mean it's improbable that others would be destroyed by it. Let the hate loose and and the doomsday machine tech that a million-world-spanning civilization will certainly have (we already have it here...) and you have the seeds to destroy any civilization no matter how large.
1 Battlefield Earth.
2 Kaiju are uber-cool, but a very inefficient way to take over a planet. I'm just sayin'.
3 This won't be a popular comment, but it's relevant to my statement. The "judgement free" generation is the most judgmental generation that's ever existed. Rather than judging ethnicity, race, sexual orientation, etc., it's judging ideas and philosophies - and the only right answer is the "judgement free" generation's answer - and anyone who disagrees is hated.