No, I'm sorry to inform you, it's not. This requires both the Wiimote and Nunchuk to play. With one hand you move the Wiimote where the icon tells you to, and the other hand you reel in the fish using the nunchuk.
If you are looking for water or fish-related games you can play with one hand, try Endless Ocean and its sequel, EO: Blue World. You can't actually go fishing, but you can get info about fish and dive.
If you want more info, you are welcome to go over to the EO and EO:BW boards. I still go to the BW board, if you ask anything on there I can answer. --- Currently waiting for: Animal Crossing: New Leaf
actually, partially out of curiosity and largely because i have an injured left wrist myself, i tried seeing how much can be done with one hand..
catching fish is actually not that hard... if you can hold both the wiimote and nunchuck in one hand (or possibly attach them together with rubber bands or something) technically you can pretty much just shake the nunchuck to reel the fish in, so you make the casting motion, wait for a bite and pull up quickly, then just shake both parts to reel the fish in...it's not perfect but it works.
honeslty the harder part is walking around since it uses the joystick on the nunchuck and the A button on the wiimote to interact with stuff.
so if you don't mind helping her out with the walking part perhaps, or maybe she could set them down for that part, using the index finger on the joystick and the ring finger most likely for the A button on the wiimote.
might want to rent it (gamefly has it) and see how well it works before investing too much money / time getting the game. (you'll probably have to order it online thru amazon.com,or gamefly)
another option, i did when my wrist was in a brace for a year.. if you can get a nunchuck with a long enuff cord (or possibly a wireless one) she could possibly learn to use the joystick with her toes...granted my family is known to have "monkey feet" anyway, but i can do surprisingly well at games with my feet. --- i tried being serious once, in 1989.. didn't particularly care for it.. so don't expect it to happen again.