Another 47 people were taken ill after drinking the brew at a gathering Sunday of the Johanne Marange Apostolic Church, a Christian fundamentalist group, near the town of Nyazura, 190 kilometers (120 miles) east of Harare.
Among the dead was a four-year-old boy.
Police spokesman Wayne Bvudzijena said foul play was suspected. He said traces of pesticide were found in containers used to make tea for the sect's Sunday gathering.
The sect, with followers across Zimbabwe, bases its teachings on Christianity alongside traditional African beliefs in ancestral spirits and the powers of tribal healers, known in the West as witchdoctors.
Forensic tests were being carried out, Bvudzijena said.
No arrests had been made.
"We are still verifying the implications," he said.