Not only can an infant not be in an exit row, but by the letter of the regs, neither can any parent of that infant (or of any child who is in the same cabin) even if the infant is sitting elsewhere. The logic for this is that in an emergency, a parent will instinctively go to the child, thereby ignoring the assumed duty of helping to get other passengers off the plane.

The only US domestic carrier that I know of that consistently enforces this part of the rule is SWA. If the FA's witness you supervising a child, they won't let you into the exit row, either. I see it often where the family boards together, and Mom sits with the kids while Dad goes for the exit row. The FA's will be really friendly and ask, "Oh, are those your kids?" Dad will say yes, and the FA will come back with, "I'm sorry, I can't let you sit in the exit row if your children are on board."