The funeral for his wife Susan is being prepared with a public memorial set for Tuesday in Harare, the capital, followed by a burial on Wednesday in his hometown of Buhera.
Tsvangirai had been travelling to a rally south of Harare when his car was hit by a lorry travelling in the opposite direction.
The Movement for Democratic Change (MDC), which he heads, has said it will conduct its own investigation into the accident to see whether there was foul play.
Britain has said the lorry involved in the fatal collision was operating as part of a joint US-UK aid venture.
The British foreign office said on Saturday that the crash a day earlier outside of Harare, Zimbabwe's capital, appeared to have been an accident and it did not suspect foul play.
"We can confirm that the truck was operated by a project jointly funded by the United States and United Kingdom," a foreign office spokeswoman said. "All indications are that this was a genuine accident."
The MDC has cautioned against speculating the crash was an assassination [AFP]
Tsvangirai left Zimbabwe on Saturday after treatment for head and neck injuries and flew straight to neighbouring Botswana for what his party officials called "proper medical check up".
Al Jazeera's Haru Mutasa, reporting from Harare, said that "the fact that he did not address hundreds of supporters outside the hospital [on Saturday] is fuelling speculation" about the cause of the crash and the circumstances surrounding it.
The MDC has cautioned against speculating the collision was an assassination attempt.
"We cannot talk of foul play ... until it has been proved what has really transpired," said Tendai Biti, secretary general for the MDC and the country's finance minister.
Biti called for a police investigation into the crash during a news conference at MDC headquarters on Saturday.
"If there had been a police escort, what happened would not have happened," Biti said. "The authorities could have avoided this omission."