Foreign observers described the poll as “very smooth” in some places and “totally disorganised” elsewhere as 5.5 million people voters were registered.
President Emmerson Mnangagwa, 75, a long-time ally of Mugabe, 94, is battling it out against opposition leader Nelson Chamisa, 40, in a tight contest.
Opinion polls give Mnangagwa, who heads the ruling Zanu-PF party, a slight lead over Chamisa, of the MDC Alliance.
Both leaders are running for the presidency for the first time in the country, which is gripped by sanctions.
Thousands of election monitors have been keeping an eye on the ballot, which the opposition has suggested is biased against them despite commission assurances.
Ellen Johnson Sirleaf, ex-Liberian president and a leader of an observer mission, said: “This is a critical moment in Zimbabwe’s democratic journey.
“The elections today provide an opportunity to break with the past.”
She said: “The lines and voter enthusiasm we are seeing must be matched by an accurate count and their choice must be honoured.”