Tsvangirai, who was the boldest opponent to longtime leader Robert Mugabe, died Wednesday in a Johannesburg hospital at age 65 after a long battle with cancer.
"Today we are paying tribute to a national hero", the acting MDC leader Nelson Chamisa president told mourners.
Mnangagwa has repeatedly promised fair elections as he seeks to attract foreign investment after years of worldwide sanctions over alleged human rights abuses.
Tsvangirai became a symbol of resistance to the ruling Zanu PF's authoritarianism, entrenched since Zimbabwe broke from its colonial master Britain in 1980.
Tsvangirai's friends from Zambia and Namibia attended the memorial service.
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"He travelled a hard journey and we should remember that".
"Let us all be united, let us be brothers and sisters and come together and mourn our former prime minister with that spirit".
Before being forced into a power-sharing deal with ZANU-PF as prime minister in 2009, Tsvangirai was beaten by police, his rallies were banned and he was charged with treason and jailed. An opposition alliance had endorsed him as its candidate, even as the ailing leader in January said he was "looking at the imminent prospects of us as the older generation leaving the levers of leadership to allow the younger generation to take forward this huge task".
Tsvangirai's body is due to be flown to his rural village in eastern Zimbabwe on Monday afternoon, ahead of his burial on Tuesday.