"He's been suffering from a thigh problem. Even if the medical checks have not shown anything worrying, we have decided not to take any chance with our best striker," Ranieri told a news conference on Thursday.
"So he will not play against Rennes."
Falcao, who did not train with the squad on Wednesday nor Thursday, was replaced in the 64th minute in last Sunday's 1-0 win at Nantes with Ranieri saying he wanted to avoid an injury.
"I knew making him play more than an hour was risky but you know the players, they always want to play," the Italian explained.
"He's been feeling some pain these past few days so I'm not taking any risk."
Falcao could be replaced in the starting line up by 17-year-old Anthony Martial, who made a considerable impact when he came on for the Colombian in Nantes.
Monaco are third in the standings with 29 points from 14 games, partly thanks to Falcao's nine goals, and lie five points adrift of leaders Paris St Germain.