The Church of England's decision to remove the legal blocks stopping women being ordained as bishops threatens its future existence, critics are warning.
Critics say the move could "threaten" the church's existence
The General Synod has voted to start the process, but it could be several years before any ordinations.
The Bishop of Southwark, the Rt Rev Tom Butler, said there were "good ecclesiological and theological reasons" for ordaining female bishops.
But opponents say the Church needs more time to consider the "divisive" issue.
Some traditionalists have warned they may convert to Roman Catholicism in protest at the vote in York.
Fourteen of the world's 38 Anglican Churches have already decided to allow women bishops.
The Church of England has had women priests since 1994 and around 400 have so far been ordained.
Supporters of women priests believe it is illogical and unfair to continue to bar them from becoming bishops.
But opponents argue there is no biblical precedent for women bishops, as Christ's apostles were all male.
They also think it is wrong for women to have authority over men in a
The Rt Rev Butler, who proposed the motion in favour of women bishops, said: "In no way can it be claimed that, in seeking at this time to test the mind of the Church of England, we act hastily or precipitately.
"I believe that there are good ecclesiological and theological reasons why women should now be able to be ordained bishop."
Opposition to the motion was led by the Bishop of Chichester, the Rt Rev John Hind, who said the Church needed more time to consider the issue.
He said the Rochester report, written by the Bishop of Rochester and published earlier this year, collated arguments for and against women's ordination as bishops.
"The Church of England has not yet had the theological debate for which the Rochester report was produced and has not agreed the principle of women bishops.
The church has allowed women priests since 1994
"There continues to be serious disagreement in the Church of England. It reveals deeper disagreements about how we do theology and agree doctrine," he said.
Father David Houlding, from the Synod Catholic Group, told BBC News 24: "The bishop is the focus of unity in the centre of mission, and it's from the bishops the church's sacramental life comes, so it really does threaten our very existence."
The vote also received a mixed welcome from MPs.
Tory MP Sir Patrick Cormack, a member of Synod, said: "I fear that a lot of people will probably leave the Church of England as a result."
But fellow Tory Julie Kirkbride said: "I am delighted by the action they have taken to bring the Church into the 21st century."
The Rev Elizabeth Macfarlane, chairwoman of the Group for Rescinding the Act of Synod, said the vote was "a step forward".
"At some point the traditionalists have to recognise that women have already been ordained as priests."