Forward Jennings, 24, scored two goals during Wrexham's six match unbeaten run in February which saw Gary Mills' side move into the play-off places.
Cheltenham Town boss Gary Johnson is the National League's manager of the month for February.
Leaders Cheltenham secured four wins and a draw in February and are currently on a 22 match unbeaten run.
Wrexham captain Connor Jennings has been named the National League's player of the month for February.