My daughter went through this, too. It drove us crazy! Here's how we handled it...
When she hits, we tell her that if she hits again she has to go to her crib. (Her crib is where we do time-outs, I'm told that that is bad, but it works for us and doesn't affect her real sleep at all.) She waits in her crib for 1-2 minutes, then we come back in. She has to tell us, "I'm sorry." If she refuses, We leave again, and come back in 1-2 minutes. She usually breaks down then if she hasn't already. Anyway, once she apologizes (we use that word with her), then we scoop her up and tell her that we love her and give her hugs and cuddles, then we talk about why she was put in "time out." She's 25 months now, and doesn't hit anymore.
I did find that when she was tired she was hitting more. You can keep a close eye on when the hitting is happening to see if your child is tired/hungry/frustrated, etc.