Tsvangirai suffered some head and neck wounds, state television reported.
The MDC, which made no suggestion foul play was involved, said Tsvangirai's wife of 31 years, Susan, was killed in the crash on one of Zimbabwe's busiest and most dangerous roads.
President Robert Mugabe visited his old rival in hospital.
They formed a power-sharing government in February after months of negotiations to try to end a political and economic crisis that has brought Zimbabwe to ruin.
"He is stable. The doctors and the family will make an announcement in due course," MDC Secretary-General and Finance Minister Tendai Biti told reporters outside the hospital treating Tsvangirai.
The crash occurred some 50 km (30 miles) south of Harare as Tsvangirai headed to his rural home in Buhera along the potholed Harare-Masvingo highway, one of the many routes neglected in the economic crisis.
State television quoted police spokesman Wayne Bvudzijena as saying:
"A haulage truck encroached into the lane of the Prime Minister's car, resulting in a side-swipe which resulted in the Prime Minister's car, a 4-by-4 Toyota Landcruiser, rolling over three times."
Bvudzijena said Tsvangirai was travelling in an MDC vehicle driven by a private, not government, driver.
Tsvangirai, who turns 57 on Tuesday, had six children with Susan, who was very popular among MDC supporters, who would chant "mother, mother" each time she appeared at rallies with her husband.
Susan, 50, avoided the spotlight but stood by Tsvangirai throughout his ordeals as Mugabe's most determined opponent. Tsvangirai has faced a treason trial and been beaten in police custody.
The tragedy came at a difficult time for Tsvangirai.
The former union leader, who was a thorn in Mugabe's side as head of the main opposition MDC, is under pressure to rescue the ruined economy.
Analysts say he may also face new political challenges from Mugabe, pushing to give his ZANU-PF party the upper hand over the MDC in the new administration.
Zimbabweans and Western donors are hoping for political stability after a power-sharing deal was reached in September.
Tensions have been rising in the new government over the arrest of MDC official Roy Bennett.
Zimbabwean police have arrested a magistrate who tried to release Bennett while his case was still before the country's highest court, a police spokesman said on Friday.
Zimbabwe's Supreme Court on Thursday granted prosecutors the right to appeal against a ruling by a High Court judge to grant bail to Bennett, a former white farmer.
The new government faces an array of problems: food and fuel shortages, the world's most serious hyperinflation and a cholera outbreak in which nearly 88,000 people have been infected, with nearly 4,000 killed, according to the World Health Organisation.
The International Monetary Fund and World Bank are expected in Zimbabwe next week to review the country's economic situation and discuss policies to address the humanitarian crisis.
South Africa is considering opening a credit line to help neighbour Zimbabwe rebuild its shattered economy after years of political and economic crisis, the Financial Mail reported.
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