Under changes which may be law before 2020, couples will no longer be given a marriage certificate at the end of a church wedding.
Instead of being asked to sign a register and certificate, they will instead sign a "marriage schedule", the Faculty Office said.
The couple then have to take this document to their local register office to record their marriage into a database and only then will they get a certificate, it added.
Failure to do this within a set time will result in the couple being compelled to "attend personally", the new law says.
Those who do not officially register their marriage will be guilty of a criminal offence and could face a fine of up to £1,000.
The government General Register Office (GRO) has not confirmed the timescale but a Church of England body said it understands couples will have only a week to register their wedding.
Rev Marcus Walker, a London-based Anglican priest, said it was "an astonishing change to the way marriages are recorded".
"What was supposed to be a fairly sensible proposal - to record the names and professions of mothers - has triggered a seriously big, and probably expensive, shift," he said.
"Now, instead of marriages being registered then and there by the priest, the couple will get a temporary certificate which they then have to present to the register office within a week of the wedding. When, y'know, they might want to be on honeymoon.
"With 60,000 religious weddings a year, this is going to result in a serious increase in the work of the registry office - and a quite significant increase in staffing, I'd imagine.
"Have they actually cleared this cost with the government or just ploughed ahead with it?"
The Faculty Office, which issues special marriage licences on behalf of the Archbishop of Canterbury, said the church has only months to train more than 20,000 clergy in the new system.
"The significant difference is that the couple will need to ensure that the marriage document is deposited at the local register office within seven days of the date of the wedding," it said.
"The couple can ask someone to lodge the marriage document on their behalf as in many cases they will, of course, be on honeymoon - but it is their responsibility, not the officiating minister's responsibility, to ensure that it is done."
A Home Office spokesman told the Times: "(The act) will mean mothers are equally represented on their child's marriage certificate. It will also modernise the way marriages are registered, moving away from the outdated paper-based system and saving over £30 million."
The Revd Dr Malcolm Brown, the Church of England's Director of Mission and Public Affairs, said: "We are in close discussions with the General Register Office, who are working hard to ensure that the change in the system of registering marriages is as smooth and seamless as possible.
"I want to reassure clergy and couples planning a marriage that we are absolutely committed to making the new system work within the context of a Church of England marriage service and the GRO has promised to provide training and comprehensive user-friendly information for clergy.
"We are currently in discussion with the GRO about the exact shape that will take and will update clergy as soon as the details have been finalised.
"Although no firm date has yet been set for the introduction of the new system we are aware of the desire to implement it as soon as possible.
"A church wedding is a very special day where unique promises are made before God and in the presence of friends, family and the wider community in a timeless setting, marking the beginning of their married lives together."
"We are in close discussions with the General Register Office, who are working hard to ensure that the change in the system of registering marriages is as smooth and seamless as possible."
— The Church of England (@churchofengland) August 9, 2019
Revd Dr Malcolm Brown, CofE's Mission and Public Affairs Directorhttps://t.co/V56MJxk32B
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