The state-run Herald newspaper said Nowak had tried to "gatecrash into the country".
The order to bar him from entering apparently came from the foreign ministry, which is controlled by supporters of Tsvangirai's rival, Robert Mugabe, the president.
"When I arrived at Harare airport I was not met by officials from the ministry of foreign affairs as before, but by immigration officials who told me that there was no clearance for my entry into the country," Nowak told Al Jazeera by telephone late on Wednesday.
"This is not the way the United Nations should be treated."
Nowak was told in Johannesburg that his visit had been postponed due to talks between mediators from the 15-nation South African Development Community (Sadc) and leaders of the Zimbabwean power-sharing government, the UN said.
Haru Mutasa, Al Jazeera's correspondent in Harare, said some analysts say the Zanu-PF may have barred Nowak because the party does not want allegations of rights abuses investigated.
"But Zanu-PF said the reason why they didn't want Mr Nowak to come into the country so soon is because they're busy with Sadc mediations ... and simply don't have time to see him," she said.
"But the MDC is saying that Mr Nowak was invited by the prime minister, and that Mr Nowak could have toured the country, done his assessment and then, after the Zanu-PF was free, they could have met him and discussed the matter."
The Sadc mediators are hoping to resolve a standoff in the government between Tsvangirai's MDC and the Zanu-PF party of Mugabe.
Tsvangirai temporarily withdrew from the power-sharing cabinet earlier this month accusing Zanu-PF supporters of human rights violations.
Opposition supporters and human rights defenders have accused Mugabe loyalists of violence, harassment and carrying out arbitrary arrests.
Nowak said he did not want to cancel the mission because he was responding to an official government invitation and the team he was travelling with had already spent a lot of UN money on the trip.
He told Al Jazeera on Thursday that he did not accept the Zanu-PF's reasons for barring him.
"I had been invited to carry out a whole mission. When I heard there would be a Sadc conference, I indicated very clearly that I was willing to change the schedule," he said.
"I can only interpret that, at this point of time, they didn't want any kind of independent fact-finding on torture and other forms of ill-treatment.
"This is totally unacceptable conduct of a government - of a member state of the United Nations - vis-a-vis a United Nations independent expert who is mandated by the human rights council to carry out fact-finding missions on the invitation of the government."
The invitation marked the first time that Zimbabwe had offered to open up to an expert working for the UN human rights council.