The opposition Keadilan party said that Saiful Bahari, one of Anwar's aides, had been arrested on Saturday and "forced" to make a statement saying Anwar had sodomised him.
The police declined to identify who had made the complaint.
Anwar has recently been stepping up a campaign to unseat the government of Abdullah Badawi, the prime minister, saying he is in a position to engineer enough defections from the ruling coalition.
Speaking to Al Jazeera on Sunday, Anwar said the accusations aganst him were politically motivated.
"This is because there is growing support for the People's Alliance [group of opposition parties] among members of parliament ... the government is under threat and there is also a lot of disgruntlement among the Malaysian public against the abuse of power and economic woes," he said.
"I have also made it known that I have in my possession, documents implicating the inspector-general of police and the attorney-general in misconduct, including the fabrication of evidence in the cases launched against me in 1998 and 1999.
Anwar said those involved had allegedly tampered with evidence.
"I fear for my safety ... my friends are very concerned for my safety. I was beaten to near death when I was in detention ... but they [the authorities] have given a flimsy statement that I will not be arrested for now."
Anwar fled to the Turkish embassy on Sunday at the invitation of the ambassador.
Ismail Omar, Kuala Lumpur's deputy police chief, confirmed the sodomy complaint but said Anwar would not be arrested "at the moment".
"We will investigate this report first. We will look into it and carry out the necessary steps before issuing any warrant of arrest," he was reported by the AFP news agency as saying.
The accusation comes 10 years after Anwar was ousted from the government in a power struggle amid accusations of corruption and sodomy.
He was convicted on both charges.
The sodomy conviction was later overturned, but only after he had served six years in jail.
Following his release, he led an alliance of opposition parties to unprecedented gains in elections in March, wresting a third of parliamentary seats and five states from the ruling Barisan Nasional coalition.
Since then he has claimed he has the support of enough members of parliament to form a new government.