Anwar’s office and the MACC did not immediately reply to requests for comment.
Anwar and Mr Muhyiddin went head-to-head in a tightly contested election in November that resulted in a hung parliament as neither candidate won a parliamentary majority.
Malaysia’s constitutional monarch, King Al-Sultan Abdullah, then appointed Anwar as prime minister after he formed a coalition with other political parties.
Since the election, Mr Muhyiddin and his party have been subject to graft investigations.
Two leaders belonging to Mr Muhyiddin’s party have been charged by the MACC with bribery over an economic recovery project launched by his government.
He was reportedly questioned by the MACC last month over a contract awarded to a relative when he was prime minister, which was said to be worth over a billion ringgit (US$221 million).
Then, he “vehemently” denied the accusation in a Facebook post, calling it an “evil slander”.
The MACC has also frozen bank accounts belonging to Mr Muhyiddin’s party.