The Argentine international was allowed home following the premature birth of his child, missing the FA Cup and Premier League matches against Stoke City in the last week.
He is also expected to miss Sunday's game against Liverpool, and will be one of a number of key absentees for a match which could have a big outcome on who finishes fourth in the Premier League.
Mancini, speaking at a news conference, also confirmed a newspaper report that he had had a disagreement with volatile Welsh international Craig Bellamy, although he denied he had sent the player away from City's training ground and told him not to return for three months.
The City manager also faces three games without veteran French midfielder Patrick Vieira after he was suspended by the FA for kicking Glenn Whelan in the midweek draw at Stoke.
"Carlos in Argentina is a big problem for us," said Mancini.
"We haven't had Carlos for a long time. Now is a frustrating time, a difficult time. It's a difficulty that in this important time for us I don't have an important player like Carlos and I have lost Patrick for three games as well.
"I hope that Carlos can come back quickly because we play Liverpool, Stoke and Chelsea. It's important for us to have all players available."
Vieira might yet face club sanctions, including a fine, for his violent conduct in the Stoke game, Mancini said.
"Patrick made a mistake, now we won't have him for three important games. It will be a problem," said Mancini. "I haven't spoken to him yet but I will."
Mancini confirmed that there had been a disagreement over the way in which Bellamy was rehabilitating his knee after injury. "I have spoken with him face to face, manager to player, but I never shouted at him," he said.
"These things can happen in your job, in my job, but I say everything face to face. I haven't a problem with him. If his knee is OK, he is available on Sunday."
