Nelson Chamisa, the MDC's spokesman, said the party's national executive committee would investigate whether foul play was involved in the incident.
Robert Mugabe, the Zimbabwean president and a long-time rival of Tsvangirai, visited him in hospital with his wife but did not speak to reporters.
'Truck hit car'
Tsvangirai had been travelling to a rally south of Harare, the capital, when his car was hit by a lorry travelling in the opposite direction, an MDC minister told the AFP news agency.
"He was hit by a haulage truck. The driver of the truck appeared to be sleeping. [Tsvangirai] was travelling to his rural home in Buhera where he was due to hold a rally Saturday," the minister said.
Haru Mutasa, Al Jazeera's southern Africa correspondent, said that Tsvangirai's car was travelling as part of a convoy at the time of the crash.
"People are wondering how this could happen if he were travelling in a convoy. Why was his car the only one apparently damaged?" she said.
"The coalition government is very fragile and people will speculate and start reading into it; they know the relationship between Tsvangirai and Mugabe was never that good to begin with."
Senior officials in the MDC have not said that they suspect foul play to be a cause of the crash, Mutasa said.
|Morgan and Susan Tsvangirai had been married for 31 years [AFP]
"MDC officials are being very careful and don't want to cause any unnecessary tension in Zimbabwe," she said.
"They do not want to make the [three-week-old] fragile coalition government any weaker than it already is."
While Tsvangirai's wife was not actively involved in the MDC, she has accompanied her husband at the party's campaign rallies over the past 10 years.
They have been married for 31 years and have six children.
Tsvangirai was sworn in as prime minister of a national unity government in February after months of political wrangling between Mugabe's Zanu-PF party and the MDC over a disputed presidential election, which the MDC claims Tsvangirai won.
The new adminstration is tasked with tackling severe food and fuel shortages, record hyperinflation and a cholera outbreak that the World Health Organisation (WHO) says has killed at least 4,000 people.