N.K.
The Y has basketball for 3 and up. My daughter just played in the league this winter.
I just skimmed the other response, so I'm now responding to it. The Y plays with tiny mini-balls and a lowered net, all specifically geared to little kids. Do get her her own little net and ball so she can see if she likes it before she commits to a league.
Sports at any age teach so many life skills that any one can benefit. Letting your daughter try something she says she's interested in could either begin a lifelong passion or help her realize that it's not her thing (at least, right now). The important thing is to make her finish whatever she starts, whether she likes it or not.
My daughter didn't like basketball, but she played in every game and learned that she has to finish what she starts (she asked to play). She is incredibly proud of her photo and trophy because it wasn't easy. She's 4.