This is not really "known" for certain. That is, it has not been established within the official Star Trek canon. We know that the Vulcans had atomic bombs by the time of the Awakening 1600 years ago (4th Century A.D.); it stands to reason that space flight developed soon after, although it is possible that a nuclear holocaust slowed Vulcan's development by several hundred years. Memory-Alpha includes an uncited claim that Vulcan was an "interstellar civilization" by the 3rd Century. I can't find the source, but this would be consistent with a 3rd-century space age ended by a 4th-century nuclear holocaust.
All we know for sure about Vulcan warp capability is that, in 2153, they had acheived Warp 7. We also know that it took them more than a century to go from Warp 1 all the way up to Warp 2. If we treat that as an average, we can estimate that Vulcan developed FTL travel in about the year 1350 AD and increased it by one full warp factor every century until the Federation's Cochrane engine finally overtook it.
The only non-canonical reference I can find is an old Star Trek RPG sourcebook, which sets the Vulcan discovery of warp drive in 1440 AD.
The best answer, then is, "Probably sometime during Earth's High Middle Ages," but this could be overruled by future canon, which could place the discovery of warp drive thousands of years earlier or as late as perhaps 1920 AD.
Either way, hope that helps!