The Communication Workers Union said it had made clear that any attempt by the company to impose change without agreement will be met with the "strongest possible opposition", including a ballot for industrial action.
Royal Mail said the pension plan was currently in surplus but it expects this to run out in 2018.
The privatised company's annual pension contributions are currently around Â£400 million.
It said that if no changes are made, the contributions could more than double to over Â£1 billion in 2018.
"We have concluded that there is no affordable solution to keeping the plan open in its current form.
"Therefore, the company has come to the decision that the plan will close to future accrual on 31 March 2018, subject to trustee approval," said a statement.
The CWU said that, in place of the current defined benefit scheme, Royal Mail plans to put all members into "inferior" money purchase alternatives.
On average, employees face losing up to a third of their future pensions, said the union.
For a 50-year-old worker earning Â£25,000 a year and retiring at 65, this would equate to a loss of Â£4,392 a year, it is estimated.
Ray Ellis, the union's acting deputy general secretary, said: "Although Royal Mail's own consultation exercise revealed massive opposition to its closure plan, the company has decided to ignore the views of its workforce and proceed with closure without consent.
"We will not stand by and watch the company abandon the pension promises it made at the time of privatisation which threatens our members with massive cuts to their future pension benefits and insecurity and poverty in retirement."
Around 90,000 workers are in the scheme.
The CWU put forward an alternative proposal for a defined benefit Wage In Retirement Scheme which it said would provide the company with "a credible, cost-efficient and lasting pension solution for all its employees".
Mr Ellis warned the company to think again, adding: "Instead of provoking a dispute by acting without agreement and closing the scheme without consent, we urge Royal Mail to withdraw its plans and enter into serious talks with the CWU to introduce our new scheme to guarantee all its employees a decent wage and security in retirement."
Royal Mail added: "We know how important pension benefits are to our colleagues. We continue to work closely with our unions on a sustainable and affordable solution for the provision of future pension benefits."
Brian Scott, national officer of the Unite union, which has 6,000 members at Royal Mail, said: "This is a cause for serious concern for a hard-working and dedicated workforce.
"The announcement is to close the two current sections at the end of March 2018 and the important part will be the replacement scheme which we are in ongoing discussions about.
"The Royal Mail Pension Plan (RMPP) is not closing in its entirety as the replacement pension scheme will embrace part of that. It is very likely that it will still be a different form of the current defined benefit scheme.
"We will study the implications of today's announcement very carefully and consider all the options going forward.
"If we don't achieve a satisfactory outcome, we can't rule out an industrial action ballot on this issue.
"We will be consulting our members closely on the next steps in the coming days and weeks."