I'm assuming that you mean a read-once transmission medium that ensures no trace of the message is left behind once it is read.
I'm also assuming that we are not dealing with in-transport security here, so that it's safe to assume that the message has been safely delivered to the recipient.
So that the only requirement is that the recipient or anyone else can't provide or accidentally leave behind any evidence of the message content.
Note that it's not possible to prevent the recipient (or a last minute eavesdropper) from copying the content as it is read. At least with modern technology. Any terminal delivery mechanism intended to transfer the message from the transport medium to the recipient's brain (e.g. audio playback or letters on a page) can reliably be captured by technological means (audio recording, photography) as it is being delivered. Even the signal from something esoteric like a direct cranial stimulation device can be recorded and used to deduce the message contents.
So let's try to ensure that a message can't be extracted from the original delivery medium (or what's left of it) after it has been read, not before, and certainly not "as" it is being read.
Unfortunately, our current understanding of information tells us that you cannot actually destroy information, as every current state of the universe depends on every past state, and given enough information about the current state, you can always trace it back into a past one. The only known way to really get rid of it is to chuck it into a black hole, and even then, you probably only send it elsewhere on a one-way trip.
But that is probably more than good enough, so that's the principle to adopt.
The principle of good enough
You can't make it impossible, but you can make it practically hard enough so that it is no longer worth it to try to reconstruct the message from the remains of the medium.
Let's think of two somewhat accessible contemporary approaches that would make it hard enough so that it is much more (orders of magnitude) expensive in terms of time, money and effort to reconstruct a destroyed message than to package it in the self-destructing medium.
Photograph your message onto film and personally print it onto photographic paper in the darkroom. Do the developer bath properly but skip the fixer/stopper bath. Dry it as it is and seal it into a light-proof envelope. Once the recipient opens the envelope, they have a few seconds to a few minutes (depending on the paper grade and the amount of ambient light) to read the message, before the paper completely turns black.
Reconstructing the message from this black paper would take a whole crew of graduate level chemistry researchers equipped with tunneling electron microscopes, looking for tiny traces of molecules being reshaped in slightly different environments. They could probably reconstruct a simple message with heuristics in about a couple of months of dedicated work. It would take a few times more effort to accurately reproduce something with precise numbers, like the coordinates of a secret installation. All assuming that the message wasn't encrypted in the first place.
Besides, if they make a single mistake in their process, they could easily destroy all their progress, and make it even harder to get back on track.
Don't forget to properly destroy your originals and negatives as well. And always encrypt your secret messages.
If this kind of activity is common in your world, there could probably be some device like a polaroid camera that works on these principles. You take a photograph of whatever represents your message, and this device produces a special print in a light-sealed envelope. The contents chemically turn dark a few minutes after exposure to light.
Deliberately defective computer memory
By design, the bit (binary digit) circuitry that holds a single one or zero in computer memory gets reset every time it is read. This is normally counteracted by rewriting the read data onto the bit circuit every time it is read. A purpose built chip deliberately lacking this rewriting mechanism would practically become a read-once medium.
A potential gotcha here is how to deliver the once-read binary data to a human. Displaying it on a screen requires additional processing and at the least holding it on some other memory in the form of pixel data. Either the whole device and software has to be of trusted design, or it could be compromised.
A simpler way could be storing digital audio in the 1-bit 192kHz Super Audio CD format or something similar on the memory, which can be converted back into a sound signal with very simple analog circuitry, involving just a capacitor, amplifier and speaker.
And the data would be gone as it is being played back.
Looking for the traces of the data on the leftover chip would be a similar effort to deciphering the photographic approach, this time employing a different set of experts and their lab.
If you encrypt the audio data, then you lose the ability to play it back directly on simple circuitry. You have to decrypt it first. Solution, there are dedicated chips for that as well.
Extra combo: Special CD-R
Let's combine the two ideas…
You could also maybe record audio on a special hyper-sensitive rewritable CD, set up to be so sensitive that the pickup laser in the player mangles it beyond recognition while reading it.
Such a sensitive CD will probably have to be transported in a sealed package as other ambient IR sources (like the sun) could easily damage it. This is all the better; if someone who doesn't know this intercepts and opens the package, they are left with just a thin circular piece of transparent plastic.
The recipient will know better, and put the disc into the player in a dark room.