The month began with an impressive three-game winning streak, which included an away victory over promotion rivals Burnley followed by back-to-back home wins over high-flying Reading and Preston North End.
The Swans drew their final game of the month at Southampton but their points haul during the month was enough to lift them to within striking distance of the play-off places in the Championship table.
Also short-listed for the January award were Jones of Cardiff City, Ipswich gaffer Magilton and Queens Park Rangers chief Sousa.
Chris Kamara, chairman of the Coca-Cola Manager of the Month Awards panel, said: "Roberto Martinez is doing a phenomenal job at Swansea City.
"They have enjoyed another outstanding month and continue to impress many in the Championship with their style of football.
"Their results in January have got them in with a real chance of being involved in the Championship promotion shake-up come the end of the season."