The Foreign Secretary risked inflaming simmering Conservative tensions over Europe by branding the proposal "unrealistic" and warning it would make the single market unworkable.
He stepped in after backbenchers wrote to David Cameron saying the Commons should have the authority to block new EU legislation and repeal measures that threaten Britain's "national interest".
Responding to the letter drafted by senior MP Bernard Jenkin, Mr Hague said in a TV interview yesterday: "If national parliaments all around the EU were regularly and unilaterally able to choose which bits of EU law they would apply and which bits they would not then the European single market would not work.
"So we have to be realistic about these things."
A Downing Street spokesman echoed his comments.
The row came as Chancellor George Osborne is preparing to use a speech on Thursday to say Britain should remain in a reformed European Union.
He will tell an audience of Conservatives the UK is gaining support as it pushes for EU changes.
The Tory leadership hit back at the party's Eurosceptic wing as a new poll showed more people think Britain should stay in the EU, but try to reduce its powers, than want Britain to leave.
Some 38% of UK voters favoured the Prime Minister's plan to limit the EU's powers compared with 28% who want to see Britain quit the Brussels club altogether, the study by Ipsos Mori for think tank British Future found.