Can a reentering nuclear warhead be stopped by a missile?

Possibly. A version of the Nike missile in the 1960s and some other systems later were designed with the intention of doing this. However it is a problem analogous to trying to shoot down a bullet shot from a gun to prevent it from hitting its target, however the reentry velocities are much higher than bullet velocities.

The most promising idea considered for this (avoiding a nuclear warhead to intercept the nuclear warhead and destroy it) uses a method called kinetic kill where the missile carried a precision guided solid metal rod 20 to 30 feet long that collides directly into the target nuclear warhead. This requires a high velocity missile and highly miniaturized computers and thrusters on the metal rod. Only preliminary tests under somewhat unrealistic conditions have been tried (e.g. the target is carrying a RADAR transponder to help guide the metal rod to collision).