Ranieri left after a weekend defeat by old rivals Juventus, their sixth loss in 10 games in all competitions, left them struggling to qualify for next season's Champions League.
The Serie A club said on their website that Ranieri had left his post and Andrea Stramaccioni, who was on the coaching staff, would take temporary charge of the team, becoming Inter's third coach of the season.
"The President Massimo Moratti and all FC International would like to thank Claudio Ranieri and his staff for their professionalism and dedication and sincerity in recent months at the helm of the team," a club statement said.
Ranieri replaced Gian Piero Gasperini who was in charge for only five competitive matches, and was their fourth coach since Mourinho's departure, the club having parted company with Rafael Benitez and Leonardo last season
"I think so," Moratti told reporters when asked if Ranieri would stay in charge for the rest of the campaign.
"Of course [the Juventus defeat] is a blow, it's also a rather undeserved defeat given the way we played in the first half, but seeing as we didn't score a goal, then obviously you can also concede."
Inter's only glimmer of hope this term has been the youth team winning a competition in London at the weekend and Moratti suggested it was time to give some of them a chance at senior level.
"I'm not the coach but I think there are already three or four who could feature for a few minutes, perhaps even more," he said.
