Anwar had been seen as the country’s prime minister-in-waiting until a reformist government, of which he was a leading member, collapsed in February amid bitter infighting.
Police called Anwar in for questioning following complaints from lawmakers whose names were included in a list that circulated online of those supposedly backing him.
Anwar said police had asked him to hand over the list of MPs but he refused on the grounds that only the king has a right to see it.
“What is mind-boggling is that they want the list,” the 73-year-old told reporters.
“This is an attempt by the political masters to oppress me — this is malicious, it is political harassment.”
Officials are investigating Anwar under two laws — one against remarks that are intended to cause public alarm, and another against sharing offensive content.
Anwar has claimed more than 120 MPs back him to become premier and that the king will meet political leaders to assess his claim.
If Anwar manages to seize power, it would mark the end of a two-decade quest for the premiership.
After their government unravelled, Muhyiddin seized power without an election, but his administration has only a two-seat majority in parliament and is highly unstable.
© Agence France-Presse