Originally Posted by 18AD
Your wrist should be pretty much straight. Is it at an angle?
Some basic stretching after playing could help as well.
+1 to the above.
OP, I'd say your problem is to do with technique. A common mistake people starting out on bass make, is to grip the neck too hard, and press down on the strings too hard. It only takes a minimal amount of pressure to fret a string. To see just how much, try fretting a string without the thumb on the back of the neck. You should not need to press down very much to get a clear sounding note. Try to keep the hand(s) as relaxed as possible. Wearing the strap too low, can affect the angle of the fretting hand (it should be as straight as possible, as stated above). Having the main body of the bass at about belt buckle height is a good comprimise, as too high will affect the plucking hand.
Below are some You Tube links, which you should find helpful.
Good luck with it.
BTW, as 18AD said, it is important to warm up (and down afterwards) with gentle stretches before even touching the bass. Below is another link for these.
EDIT : Just realised that you stated you were a lefty, so you are talking about the plucking hand
The clips and info above are still valid though, and worth taking on board. Here is yet another clip, this time on right hand techniqie.
Sorry about my mistake.