This is common when you just start out, but it is better you give your wrist a bit of rest when things start hurting. Also, try to use less force when gripping your ukulele. You only need to put so much pressure that the chord sounds clean, anything more is wasted energy.
If you find a particular chord difficult to hold, resulting in too much pressure to compensate for the bad grip, try slanting your hand position in the direction of the neck (so your fingers point slightly towards the body, instead of being at a straight angle to the neck), this may help a bit. Be sure to take a break between sessions, stretching your hands a bit as well.
Edit: oops, too late and hey, there was a thread already! Had forgotten about that...