"We never arrested him," Wayne Bvudzijena, a police spokesman, said.
Tsvangirai, who leads the Movement for Democratic Change (MDC), had been due to give a press conference on the alleged abduction of a party activist.
Speaking on state television news, Bvudzijena said police had searched the opposition party headquarters in Harare and arrested only 10 people, who they said were linked to what the government calls "democratic resistance committees".
Bvudzijena also said that Piniel Denga, an opposition official, had been arrested in a raid on his home on Tuesday night and claimed that police uncovered 53 sticks of dynamite and 35 detonators and various documents in the raid.
Bvudzijena said eight suspected members of the opposition party were also arrested at various different locations.
"We are not witch-hunting. We are carrying out investigations and they are very thorough," he said.
Alec Mmuchadehama, a lawyer acting for the opposition, said the opposition legal team had been denied access to those detained.
"We have been given no access to those arrested. We believe they are scattered in police stations around Harare," he said.
Activists assaulted
Tsvangirai and a number of MDC activists were detained and assaulted two weeks ago while trying to stage an anti-government rally.
Southern African leaders at the 14-nation Southern African Development Community (SADC) summit, to be held in Dar es Salaam on Wednesday, are expected to address the growing crises in Zimbabwe.
Tanzanian officials said SADC leaders will try to convince Robert Mugabe, Zimbabwe's president, to meet leaders of the opposition Movement for Democratic Change (MCD) in a bid to resolve a situation that threatens to destabilise the country.
Hebson Makuvise, an MDC official, told Al Jazeera: "We hope they [the SADC leaders] will come up with a clear message for Mugabe that what he's doing is not acceptable.
"They should condem him publically. What he is doing is not good for the region, it's not good for Africa and it's not good for Zimbabwe."
Jonathan Moyo, information minister in Zimbabwe until he fell out with Mugabe in 2005, told Britain's The Guardian newspaper that regional leaders at the conference would go further and tell Mugabe that he must retire when his term expires next year.
He said: "They will remind Mugabe that he told them he would retire at the end of this term in 2008. They will tell him he must do that.
"The statement issued at the close of the summit will not strongly condemn Mugabe - that is not the way SADC works. But I am certain that in the meeting the leaders will have told him in no uncertain terms that he must retire."
Use of force
Despite the assault, Tsvangirai has continued to call for the removal of Mugabe, who has been unapologetic about the use of force by his security services.
Talking to journalists after a memorial service on Tuesday for an MDC activist who was shot dead on March 11, he said that the assaults had served to unite opposition against Mugabe.
Tsvangirai said: "You can see that everybody is united and is mobilised and confronting the dictatorship.
"There is no dictator in this world who has succeeded to oppress the people forever ... We cannot dignify an old man who has lost his mind."
The SADC conference, hosted by Jakaya Kikwete, the Tanzanian president, is also expected to address troubles in the Democratic Republic of Congo, where government forces clashed last week with fighters loyal to Jean Pierre Bemba, a former vice-president and unsuccessful presidential contender in last year's elections.