The 33-year-old Mali international, who counts Swansea and Gillingham among his former clubs, enjoyed a stint with Sheffield Wednesday in the npower Championship earlier this season.
Sidibe made six starts and four substitute appearances for the Owls, scoring once and playing his first football in more than two years following an injury nightmare consisting of severe Achilles and knee problems.
He is available to make his debut on Saturday when Tranmere look to get their promotion push back on track at Colchester.
Manager Ronnie Moore said: “I’m delighted to bring Mamady in on loan, he’s the big target man I’ve been looking for and we have beaten quite a few teams to get him.
“He’s an experienced striker who leads the line well. He will cause defenders problems and at six foot four he will give us extra height defending set pieces too.
“I think he can do a really good job for us at this level and he is a big signing for the Club. I’m grateful to Tony Pulis for allowing Mamady to come to us.”
St Johnstone manager Tommy Wright has accused Neil McCann of deflection tactics as he denied reporting the Dundee boss to the Scottish Football Association.