McDermott's side were beaten 3-1 at Tottenham in their opening fixture of 2013 but remained unbeaten for the remainder of the month.
The Royals won two of their four Premier League fixtures, beating West Brom and Newcastle, and held Chelsea to a 2-2 draw at the Madejski Stadium.
Le Fondre started all four Premier League games on the bench but netted five goals with doubles against Newcastle and Chelsea and a penalty against West Brom.
Reading also won both of their FA Cup ties, beating Crawley 3-1 in the third round on 5 January and seeing off Sheffield United 4-0 three weeks later to set up a fifth round clash with Manchester United.
Le Fondre told the club's official website: "It is a fantastic achievement for me, it's madness really. Just to think where I have come from and then to pick up this award, it goes to show what the hard work I have put in amounts to - I'm buzzing from it!
"When the gaffer told me I really didn't know what to say. It's quite mad really when you look at the other strikers in the league; Suarez, Van Persie, Aguero, Rooney etc. and so for little old me to win Player of the Month is fantastic."