The Palestinian move on Tuesday came soon after Jordan called for the dismissal of Patriarch Irineos I for allegedly seeking to lease out church properties in east Jerusalem to a Jewish group.
"We are in full coordination with the Jordanians," a Palestinian official said. He said the decision would have to be endorsed by Palestinian leader Mahmoud Abbas, who was travelling in South America.
The patriarch's deal has infuriated Palestinians, who claim east Jerusalem as capital of a future state.
Israel, the Palestinians and Jordan traditionally grant recognition to the Greek Orthodox patriarch. It wasn’t immediately clear what effect the withdrawal of Palestinian recognition would have on Irineos, who has rejected calls to resign.
Irineos' opponents in the Church said last week that they decided to dismiss him. But Irineos' supporters said the vote was invalid. The patriarch can only be ousted by the church's highest decision-making body, the 17-member Synod.
Archmandrite Atallah Hannan, a church spokesman and critic of Irineos, praised the Palestinian cabinet's decision.
"We thank and salute the Palestinian government for its position and we hope that President Mahmoud Abbas will adopt this position," he said. "The decision to dismiss Patriarch Irineos was taken by the majority of the members of the Synod."
Israel has said it would not intervene in the feud. Irineos denies any involvement in the land deal.