Actually, no! Einstein won the Nobel Prize in Physics in 1921, but it was specifically for his explanation of the photoelectric effect, not for relativity. 

The Nobel Committee was quite cautious about relativity at the time - it was still considered somewhat controversial. The photoelectric effect work, which showed that light behaves as particles (photons) and helped launch quantum mechanics, was seen as more experimentally verified and less contentious.

It's one of those interesting historical ironies - Einstein is most famous for relativity (both special and general), but his Nobel Prize was for different work entirely!
