Eleven people in Harare and 20 from Mashonaland Central said Zanu-PF supporters attacked them one day after the results of Wednesday's election were announced.
Those in Harare said they had to seek refuge from the attackers at MDC party headquarters Sunday, the BBC reported Monday.
MDC supporters in Mashonaland Central province said Zanu-PF supporters went door-to-door ordering them to pack their bags, take their families and leave.
The alleged attacks come after MDC candidate Prime Minister Morgan Tsvangirai called the presidential election fraudulent and vowed to contest the results.
MDC Treasurer Roy Bennett called for "passive resistance" after the results were announced.
"I'm calling on the people of Zimbabwe, who are our constituents and who we represent in the positions we hold, for passive resistance and for total disengagement," he said. "And let Zanu-PF rule and rule by themselves and bring the country to a standstill."
The Zimbabwe Election Support Network, a local monitoring group, said the election had been "seriously compromised" because as many as 1 million people had been unable to vote.
The election was fair and free "from the campaigning point of view," said former Nigerian President Olusegun Obasanjo, head of the African Union mission.