The Paraguayan striker aggravated a problematic calf injury during City's 2-0 away defeat at Everton on Saturday evening.
"It looks like a bad injury for Roque," City boss Roberto Mancini has told the club's official website.
"It is to the same calf that was a problem around Christmas.
"It could be around one month, we don't know exactly when he'll be back yet. It does not require surgery, just treatment."