"Falcao continues to nurse a (thigh) muscle pain. It has been improving but he still cannot take part in the next game," Monaco said in a statement.
Colombia forward Falcao, who has scored nine goals from 14 league outings, has not played since a 1-0 win at Nantes on November 24.
He joined Monaco during the close season from Atletico Madrid for a 60 million euro ($82.74 million) transfer fee.
His absence has been widely commented on by sports daily L'Equipe, with Falcao even making the paper's front page on Thursday.
"The Falcao mystery", ran the headline, followed by two pages of speculation on the striker's absence, including a question as to why the striker was not wearing the Monaco shirt on his latest Twitter profile picture.
"It is tricky to speculate on the evolution of the situation with this kind of old injury," coach Claudio Ranieri told a news conference, referring to Falcao's injury dating back from last season.
"I have been annoyed by what has been said but it's normal, it's football. Anyway, people talk about Monaco."
Without Falcao, Monaco have won their last three Ligue 1 games, with Emmanuel Riviere and Anthony Martial looking sharp up front.
Monaco are second in Ligue 1 with 38 points from 17 games, two points behind French champions Paris St Germain. ($1 = 0.7251 euros)
(Reporting by Etienne Ballerini; Writing by Julien Pretot; Editing by Alan Baldwin and Justin Palmer)
