"The Reds thank him for his services and congratulate him on winning the Gaucho championship," they added, referring to the state championship played in the first third of the season.
The club's Under-20s team coach Clemer was put in charge as caretaker for Sunday's match against Fluminense.
Dunga, whose team won 26 and lost nine of their 53 matches, was sacked when they were still in Rio de Janeiro where they lost 3-1 to lowly Vasco da Gama on Thursday.
Inter have slipped down the standings to 10th place with 34 points from 25 matches, 22 points behind runaway leaders Cruzeiro. Vasco's win lifted them one point above the relegation zone.
Dunga, who lost the Brazil job after his team were eliminated in the quarter-finals of the 2010 World Cup in South Africa, took charge at Inter at the beginning of the year.
It was the 49-year-old's first job as a club coach with the team where he started and ended his playing career as a midfielder.
Abel Braga, who steered Inter to the Libertadores Cup and Club World Cup titles in 2006, is being touted as favourite to take over.
(Reporting by Rex Gowar in Buenos Aires, editing by Ed Osmond)
