McClaren won out over fellow nominees Nottingham Forest manager Billy Davies, Birmingham's Lee Clark and Ipswich boss Mick McCarthy.
Derby were unbeaten throughout the whole of last month - winning six out of seven league games - and drawing the other one as they climbed into the upper reaches of the table.
McClaren said: "Like I've said from my very first day here, it is the players that cross the white line. They perform and they take the responsibility on the pitch.
"They have to also take on board what we've worked on during the week and our results and performances suggest they've done just that.
"As a result of that happening we have been getting both results and recognition.
"I've always seen this award in the past and thought 'it's not just about the manager' - and it's very much the case now I've been presented with this award.
"It is about all the staff and I can't stress how important they are."
Brentford boss Mark Warburton took the honours in League One.
The Bees won all four of their games last month after Warburton succeeded Uwe Rosler at Griffin Park, a run which saw them move to the top of the standings.
Cheltenham manager Mark Yates claimed the League Two prize after his side took 10 points from five games in December.
Leicester midfielder Danny Drinkwater is the Sky Bet Championship player of the month with midfielder Sam Saunders completing a double for Brentford with the League One player of the month award.
Scunthorpe striker Deon Burton netted the spoils in League Two after scoring four goals in as many games in December.