Tsvangirai died in South Africa, where he was being treated for colon cancer at a hospital in Johannesburg.
Tsvangirai had a tumultuous and era-defining career in Zimbabwean politics.
An MDC spokesperson said that "we should brace for the worst".
The eldest of nine children, Tsvangirai worked at a textile mill in Mutare in the east, and later joined a nickel mine in Bindura, a town in the country's north.
Mr Tsvangirai founded the MDC in 1999, after a decade as the Secretary General of the Zimbabwe Congress of Trade Unions.
Perhaps the most instantly recognizable image of Tsvangirai are the grisly pictures of a beaten Tsvangirai were seen around the world in 2007 when police detained and beat him for organizing a protest in Harare. In 2000 the MDC rattled Mugabe's Zanu-PF by coming within a few seats of beating it in parliamentary elections.
He recently stood and was accepted by the MDC-T and its allied parties as its presidential candidate for elections later in 2018, even though he knew he was terminally ill.
In 2002 a doctored video surfaced of Morgan Tsvangirai purportedly plotting with a former Israeli intelligence agent to assassinate Mugabe.
Tsvangirai claimed to have won a majority and said that the results could have been altered in the month between the election and the reporting of official results.
A party that tried so hard to unseat former President Robert Mugabe for decades before a military coup ended his rule late a year ago.
His first wife, Susan, was killed in the head-on collision. Tsvangirai walked away from crash, but Susan was killed.
After running in a tightly contested election against Mugabe in 2008, Tsvangirai pulled out of the second round voting, stating a free and fair vote was impossible as his supporters faced violence and imprisonment at the hands of Mugabe's security forces. He alleged widespread fraud but withdrew a legal challenge to overturn the outcome.