The short answer is that memes exist as far back as human civilization, by definition. Unfortunately, that answer is based on the technical definition of meme, which you are probably not looking for.

Richard Dawkins coined the term meme to describe any replicated cultural idea or belief. Interestingly, they are just as subject to evolution and natural selection as living things. Mutating through being passed on through generations and among populations.

Basically, he envisioned it as the basic functional unit of transmitted culture to contrast biologically inherited genes.

Of course, most people probably think of a meme as an image macro with humorous text and variations on a theme. If that's what you're looking for, then you can certainly find silly captioned photos of cats, going back to the rise of modern photography. I don't think io9 is the best source, but it contains quite a few examples from early photography. However, these were probably not likely to be re-captioned and re-circulated given the technology at the time didn't allow for effortless duplication.

Hopefully someone else here can provide insight into possible earlier examples predating photography.