It'd completely ruin scientists' day.
(Maybe even an entire week)
Imagine for a minute Earth in its current shape. You know energy can't just appear or disappear. It has to go somewhere, be it in the form of heat, motion or light (not just visible, the whole electromagnetic spectrum counts for this purpose). You also know mass/matter can't just appear or disappear. It's a comfortable, stable place.
Then magic is thrown into the mix. Suddenly energy can be generated out of thin air. Matter can be created, manipulated (which would always require energy) or be vanished (Which conflicts with conservation of mass). Not to mention the existence of different planes of existence in the D&D realm from whence a conjurer summons his creatures would pretty much ruin everything we know about the universe (or in this particular case, the multiverse).
With our current sets of natural laws in place, making matter "appear" would require obscene amounts of energy. Following Einstein's E = MC² equation we can extrapolate the energy required to convert energy to mass in the current reality. The equation in this form only works for matter in a 0 energy state. (So your matter would be 0K in this example.)
For one gram of matter to be "made" out of energy roughly ~1.8×10^14 joules is needed. To give you an idea how much that is, a kiloton (1 million kilograms) of TNT exploding would generate 4.184×10^12 joules. Almost 2 orders of magnitude less than the energy needed to make a single gram of matter out of energy.
Now we covered the nasty reality interfering aspects, it's time for better news. In D&D lore it's said there is a "weave" from which people (mainly arcane casters I believe) draw their magic. Without going all too deep into strings building up particles and the like, it could simply be stated that some people with a certain gene expression could interact with this weave.
In our own reality there is plenty of mystery left to employ in this particular situation. A cloud of dark matter could have collided with Earth making for all sorts of whacky reactions, perhaps this could be your source of the strange interactions so different from the normal laws of physics.
Divine spellcasters might still pose a problem. You haven't specified in your question whether or not a god or multiple deities are present in your setting and honestly I have no idea how to explain this away other than "somehow these deities can now exert their influence here."
Maybe their sphere of influence is confined to the bounds of the dark matter area mentioned above.
Things get really strange when D&D magic is being tossed in the mix with the actual laws of physics. Hopefully this will give you some ideas which direction you can take with your approach. This surely isn't the only way to deal with this situation. I bet some other creative souls on this site could help you come up with some other really cool ideas. But I hope it helps you regardless.