In the latest incident, sixteen churchgoers, including an elderly woman, were arrested and detained, and several priests turned out of their homes in the Diocese of Harare.
The Anglican Church of Zimbabwe has faced attacks, police raids and random arrests since the excommunication of former Bishop of Harare, Dr Norbert Kunonga.
Dr Kunonga, a staunch ally of President Robert Mugabe, was excommunicated in 2007 after trying to withdraw the Diocese of Harare from the Anglican Church of the Province of Central Africa (ACPA).
He has attempted to establish a rival church and seized property belonging to the ACPA.
On Sunday, representatives of Kunonga tried to evict two priests from their houses. When his henchmen turned up again on Tuesday night to turf another priest out of his home, some members of the priest's congregation seized the attacker and took him to the local police station.
The police, however, sided with Kunonga and went to the house to arrest the church members.
The interference has alarmed the Bishop of Harare, the Rt Rev Chad Gandiya, who said the arrests were illegal.
"I am really concerned about this," he said.
The bishop said the diocese would seek bail for the churchgoers "if the police will listen". He asked for prayers for the churchgoers, who remain in prison, and their families.
Bishop Gandiya said: "Please pray for our registrars as they try to sort out their bail. Pray for those arrested. Pray especially for the families of all who were arrested last night.
"They are greatly traumatised by all this. I am told by some of my priests about their children who are affected and are worried about their fathers. Please continue to pray for us as a diocese."
Concern for the Zimbabwean Church has been voiced by the UK-based mission agency USPG, where Bishop Gandiya was formerly a regional manager.
USPG Chief Executive Janette O'Neill said: "We are deeply concerned at the increased level of threat and harassment being levelled at faithful members and clergy of the Anglican Church – especially by the forces of the state that should be there to protect and serve the people.
"We will support Bishop Chad through prayer, advocacy and practical means as he upholds both human rights and the legal right of the Anglican to minister to its communities.
"He is their champion and cannot submit to these threats and actions resulting from the illegitimate claims of Mr Kunonga."