Andrew Tyrie, chairman of the Treasury select committee, said insufficient evidence had been produced to justify the "hugely expensive restoration project".
The project could cost up to Â£4bn and take five to eight years to complete.
MPs and peers had warned the palace risks a "crisis" without repairs.
Parts of the Palace of Westminster are so badly affected by asbestos, fragile stonework and ageing electrics and wiring, it has been said the Grade I-listed building would be knocked down if it was not protected.
In a report last year a joint parliamentary committee of MPs and peers appointed to examine the refurbishment options  recommended that all MPs and peers should vacate both Houses of Parliament for six years during the works, and said the plans must not be delayed any further.
Chris Bryant, a Labour MP on the committee, said: "All the evidence points to having to move out of the whole palace simultaneously. That is the lowest-risk, most cost-effective and quickest option."
Speaking about the launch of the inquiry, Mr Tyrie said: "Neither the report by Deloitte, nor that by the joint commission, provides enough of the evidence needed to come even to a preliminary decision on these proposals - so the Treasury committee will attempt to collect some of it.
"This is why the committee has called for evidence on this massive, and hugely expensive, restoration project.
"The proposals certainly need thorough scrutiny."
Last month Mr Tyrie wrote to the leader of the House of Commons David Lidington MP to ask for further details on relocation options, potential risks, and costs for the project.
A Commons vote on whether to press ahead with a full or partial evacuation is expected in the comings weeks.
MPs have launched an inquiry into the planned renovation of the Palace of Westminster amid concerns it may not provide value for money.