The 25-year-old scored four goals in four league appearances last month, including a brace against Swindon Town, to help the Sky Blues climb to within one point of the playoffs.
"It's great to see Marc being recognised for the hard work that he puts in week in week out and he is a deserved winner," Coventry manager Mark Robins told the EFL website.
"His performances have been outstanding and his goals have been vital for us, so congratulations to him and let's see if he can push on again and win the award in February as well."
McNulty added: "It's the first time I've picked up one of these awards so it's very pleasing to receive it. I went on a little run in December, and as a striker you take a lot of confidence from scoring goals and it's just gone from one week to another.
"I think the boys have just been a little bit inconsistent this season, we know that ourselves but there's still a lot to play for, there's still a lot of games and we're positive that come the end of the season we'll do well."