He was giving a lecture in Harare to mark two years of power-sharing with Mugabe’s party, but relations between the two partners are worsening.
Police said the car had a blue beacon-light that was only permitted on police, military and presidential vehicles.
Prosecutors said the drivers were a threat to national security, and the men were only released on bail after three nights in custody.
This is not the first time Tsvangirai’s vehicle has been impounded: last time it was ahead of the second round of presidential elections in 2008.
His MDC party fears that elections this year spark similar violence to that experienced in 2008, when more than 200 people were killed.
At least 12 people have been injured in clashes between MDC and Zanu-PF supporters in the last month. Police blame the MDC. Tsvangirai said in his lecture that Zanu-PF is willing to inflict violence on Zimbabweans.
He said he was launching a global campaign to ensure Zimbabwe holds free and fair elections.
Prime Minister Morgan Tsvangirai has blamed President Robert Mugabe for the current politically-motivated violence he says is being perpetrated by members of the uniformed forces because the President is answerable for their actions as the Commander-in-Chief of the Defence Forces.
Tsvangirai told a public meeting in Harare on Tuesday that President Mugabe sought to exonerate Zanu PF from the disturbances claiming there was no violence in the country.
“We have a structure where we have a Commander-in-Chief who purports not to know what is happening, but indirectly orders the army to act. The buck stops with (President) Mugabe. If they (uniformed forces) defy his orders against violence, then we can say we have a coup in the country of which I don’t believe there is one,” he said.
“It’s not sharing in commanding, but in responsibilities and hopefully when he comes back (from Singapore) we will deal with that.”
President Mugabe is in Singapore where he is receiving treatment for an eye ailment, the nation has been told.
“Over two years they (the uniformed forces) have failed to adjust and refused to let go of their partisan actions,” Tsvangirai added. But presidential spokesperson George Charamba said the police have a position on the matter.
“Wait for the President to come and he’ll talk on that,” he added.
The PM poured cold water on speculation the inclusive government, which turned two years on February 11, had outlived its lifespan saying the three-legged coalition would trudge on despite the stumbling blocks.
He ruled out talk of an election being held this year saying those that said so were misrepresenting facts.
“The issue of the GPA expiring is a matter of public concern, but it has been misrepresented left, right and centre,” Tsvangirai said.
There is nothing that stipulates a time period. There is no sunset clause for the GPA and last week when we had a National Security Council meeting, someone was trying to mislead us that there would be elections in 2011 and we said where are you getting that from? Certain actions will kill the inclusive government but that would need lawyers to interpret.”
He went on: “The inclusive government will end if a certain process is instituted and a new constitution is in place then the President and the Prime Minister will set the date for new elections.” Tsvangirai said the public media was promoting hate, division “and even genocide”, threatening national security.
“The public media can go for years singing (President) Mugabe ane monya (President Mugabe has bouncers) but once the mood of the people is shifted, you cannot stop them,” the former trade unionist said.
“The major lesson from Tunisia and Egypt is the sanctity and eventual triumph of people power. Parties that have lost the support of the people have no power to hang on. The eventual time of people power will come.”
Zimbabwe’s 2011 agenda, Tsvangirai said, was to mobilise national, regional and international support for a road map that would guarantee a free and fair election. The people had the right to reject the Copac-led constitution-making process which had failed the test of legitimacy, he said.