A report from the Public Accounts Committee (PAC) has questioned how the policy will be funded, and whether proper replacement homes will be built.
The MPs also said there was evidence that Right to Buy could increase overcrowding for those in housing need.
The government said it made no apology for encouraging home ownership.
The idea of the scheme is to allow Housing Association tenants to buy their own homes, with discounts similar to those currently enjoyed by council tenants.
Members of the Committee said there was also a danger that increased discounts for Housing Association tenants would lead to greater fraud.
Meg Hillier, chair of the PAC, said the approach to paying for the policy was entirely speculative.
"There are no costings or workings out. We are not talking about a 'back of an envelope' calculation - there is no envelope at all."
The policy has previously been criticised by the Local Government Association, and the Institute for Fiscal Studies (IFS).
It has also been rejected by the governments of Wales and Scotland.
The government has said that the extension of Right to Buy - which is already being piloted in five areas of England - will be funded by councils selling off their most valuable council houses.
It promised that all the homes would be replaced.
But the MPs concluded that the government's commitment "will not ensure that these will be like-for-like replacements".
They said new homes "can be a different size and in a different area, and may cost more to rent".
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In their report, the MPs also said it would be difficult to replace homes on a one-for-one basis. They said such a target would require a five-fold acceleration in housing starts.
As a result, the policy could "lead to those in need of social housing suffering greater overcrowding."
But the government insisted that all the replacement homes would be built.
"This government makes no apology for helping people into homeownership," said a spokesperson for the Department of Communities and Local Government (DCLG).
"Our voluntary agreement with housing associations will mean 1.3 million tenants will have the chance to own their own home, while every home sold will be replaced with a new affordable property."
The scheme is due to be rolled out across England later this year.

There was an initial outbreak at Weston General Hospital before Christmas and then a fresh outbreak afterwards.
Uphill and Berrow wards are now both open and the Ashcombe maternity unit is fully open for expectant mothers.
A third ward, Kewstoke remains closed and still has restrictions in place, hospital bosses said.
When there was an increase in emergency admissions over the Christmas and new year period,  eight out of 12 beds in the maternity unit were used for admissions but now it has returned to being fully used by the maternity unit.

Farieissia Martin, 22, had denied killing 21-year-old Kyle Farrell, who was knifed in the chest at the house in Charlecote Street, Dingle.
But a jury at Liverpool Crown Court found Martin guilty. She is due to be sentenced on 9 June.
Mr Farrell died in hospital after suffering a single stab wound early on 21 November 2014.
His family said he was a "devoted father and loving son" who will be missed by all his family and friends.
The government's controversial plan to extend the Right to Buy to Housing Association tenants has been sharply criticised by a group of MPs.
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Two wards at a Somerset hospital have been reopened to admissions after an outbreak of norovirus at the end of December.
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A woman accused of stabbing a man to death at her house in Liverpool has been convicted of murder.