Tsvangirai’s party insisted it would carry out its own investigation into the collision with a truck carrying aid paid for by Britain and the United States which the British government called a "genuine accident".
Botswana’s Foreign Minister Phandu Skelemani said Tsvangirai would get a second opinion on his condition at the private clinic in Gaborone.
A decision to fly Tsvangirai out of Zimbabwe was taken after Botswana’s President Ian Khama sent Skelemani and other officials to visit him in hospital in Harare on Saturday.
‘He needs his friends’
Tsvangirai, who suffered neck and head injuries, was seen walking out of the Avenues Clinic in Harare on Saturday accompanied by MDC ministers.
"We went there because Tsvangirai had lost his wife. The president (Khama) sent us there to deliver condolences, and went to see him at the clinic," said Skelemani.
Khama is a strong supporter of Tsvangirai and has openly criticised Zimbabwe’s President Robert Mugabe. Before joining a unity government with Mugabe, Tsvangirai stayed in Botswana for two months, returning on January 17 to resume power sharing talks.
"As Botswana government we grieve with Tsvangirai. He needs to know that his friends are around him and they feel for him, and that is the sort of support we are showing him," Skelemani told AFP.
Tsvangirai was travelling with his wife on Friday when their car collided with a truck carrying foreign aid and rolled several times. Susan Tsvangirai, 50, died at the scene.
A spokesperson for Tsvangirai’s Movement for Democratic Change (MDC) said it was not known when he would return to Zimbabwe.
The MDC has vowed to launch its own investigation and, although officials have not suggested foul play, the MDC number two, Finance Minister Tendai Biti, indicated that a police escort might have prevented the accident.
"Police are making their own investigation, we are also making our own," Biti said, adding about the escort: "The authorities could have avoided this omission."
Tsvangirai’s car was hit by a truck which crossed into the oncoming lane and side-swiped the prime minister’s vehicle, causing it to roll several times, police said.
Britain has confirmed that the truck was owned by a joint US-British aid project that delivers HIV/Aids drugs. It denied reports that the driver may have fallen asleep.
"The driver was not asleep, he was well rested and had not been drinking," a foreign office spokesperson said. "We cannot pre-empt any investigation by giving further details at this stage."
An MDC minister had told AFP earlier that the truck driver "appeared to be sleeping".
President Robert Mugabe and his wife Grace visited Tsvangirai in hospital on Friday evening and later sent a letter of condolence.
The accident has raised new concerns about the fragile unity government whose inception has been plagued by disputes over the appointments of top officials.
"The accident has presented a very challenging hurdle for the Zimbabwe fragile accord," said Daniel Makina, an analyst based at the University of South Africa.
"People are not going to stop speculating and will probably start pointing fingers. Unfounded and damaging speculation could be disastrous."
Tsvangirai claims to have been the target of four assassination attempts including one in 1997 when he said assailants tried to throw him out of his office window. He has also survived a severe beating by security forces.