The IOC's executive board also froze contacts with and financial payments to the International Amateur Boxing Association (AIBA), whose interim president has been named as a leading criminal by the US Treasury Department.
The board said it was "not satisfied" with a report by AIBA about its governance, refereeing and anti-doping issues, and demanded a further report by April 30.
"The IOC reserves the right to review the inclusion of boxing on the programme of the Youth Olympic Games Buenos Aires 2018 and the Olympic Games Tokyo 2020," a statement said.
"This decision is extremely disappointing for AIBA as it hoped the IOC Executive Board would have understood that the processes necessary to implement even more measures require more time," the statement said.
IOC president Thomas Bach said AIBA had been asked to provide more information about accusations of fixing at the Rio Olympics, where a group of officials were sent home following a number of controversial decisions.
"We are still looking into this issue... we want them to (give) a satisfying explanation," Bach said, adding: "We are extremely worried about the governance of AIBA."
Rakhimov, 66, came to power last month following the abrupt resignation of Italy's Franco Falcinelli, who was briefly interim president after Taiwan's Wu Ching-Kuo stepped down in November.
"Our message to the IOC and to the world of boxing is that AIBA is turning over a new leaf and we intend to demonstrate our responsibility to all national federations and our commitment to the sport we all love," Rakhimov said in an AIBA statement last week.
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