Leicester recorded four league wins and a draw during the month. Oakley featured in each game and scored in the 3-0 home defeat of Leyton Orient.
"I am very pleased to win the award. The team has been doing very well and I am enjoying my football at the moment," Oakley told the club's official website.
"We hope to share the award around the dressing room if we keep winning and picking up the points towards the promotion we are all after - and it will help with the banter in training.
"I have been taking a bit of stick from Lloyd Dyer and Andy King about them scoring more goals, so I am glad to have got the first award on the board."