The phrase in question is part of a news article's headline:
Letters: Turkey’s attack on a Russian jet came after one provocation too many.
I googled the phrase but it doesn't seem to exist in any dictionary. However, I came across "have one too many" which refers to drinking too much alcohol. Therefore, I'm guessing one provocation too many means too much provocation. But, if my guess is correct, what does the word one refer to?
You're totally spot on. This is a play on the idiomatic expression one too many. When people say one in the right context, one usually refers to a bottle of an alcoholic beverage such as beer. For example, in a bar (or a pub if you're in Great Britain), you could ask the bartender for a cold one and your request would be understood as that you want to buy a bottle of beer. cold comes from the fact that beer is typically served cold. And that's how these two expressions are related.
But let's get back to the idiom one too many. First of all, it has a rather negative connotation. The idea here is that if you've had one too many, then you've probably drunk more alcohol than you should have which might lead to negative consequences such as killing someone while driving under the influence. Now it's not that difficult to make a connection between this idiom and what they're saying in the sentence. One provocation too many is meant to imply that there had already been a number of provocative actions on Russia's part and that last one when a Russian fighter jet violated Turkish airspace really crossed the boundary (no pun intended) and led to a situation where the Turks finally had to take serious measures—the aircraft was shot down.
By the way, you could alternatively say that this incident with the fighter jet was the last straw for the Turks. One just can't help but think of this great English expression when reading your post.
We have an expression "the straw that broke the camel's back." That straw is "one straw too many."
We use the "one too many" idea in the context of small issues of one kind or another that accumulate. Finally, one more issue gets added and it becomes more than the entity who is dealing with the issues can handle.
So, someone who has had "one too many" has had several drinks, and has now had one drink more than he can handle and has become drunk.
With your sentence, suppose a Russian jet flies over Turkish airspace, and the Turkish feel provoked but do not retaliate. The Russians do it several more times, and the Turkish feel increasingly provoked, but still do not retaliate. Then, the Russians fly one more jet over Turkish airspace, and that is "one provocation too many," so the Turkish retaliate.
This isn't to say automatically that the provocations were all the same thing; I'm just making up a scenario that demonstrates the idea in simple terms.
