The free vote was due to take place on Wednesday and if carried, would have brought hunting laws in England and Wales into line with Scotland.
Scottish nationalist MPs do not normally vote on matters that only affect England and Wales, but Scotland’s First Minister and SNP leader Nicola Sturgeon said they would do so on this occasion.
With Labour and SNP opposition, the changes would almost certainly have been defeated if the vote had gone ahead because of the Conservative government’s small majority.
Ms Sturgeon linked the move to to the government’s plans for “English votes for English laws”, known as Evel, which would give English MPs a veto over England-only legislation at Westminster.
She told BBC Radio 4’s Today programme: “The English votes for English laws proposals brought forward go beyond any reasonable proposition and look to make Scottish MPs effectively second-class citizens in the House of Commons.
“So if there is an opportunity, as there appears to be here, and on an issue where David Cameron appears to be out of touch with majority English opinion as well, to actually remind the government of how slender their majority is, that is an opportunity we will take.”
Opinion polls show a big majority against foxhunting in the UK.
SNP Westminster leader Angus Robertson said the Scottish parliament would consider toughening the law on foxhunting north of the border.
Foxhunting is illegal across England, Scotland and Wales, but for pest control reasons, hunts are allowed to flush out foxes so they can be shot. In England and Wales, only two dogs can be used to do this, whereas unlimited numbers are allowed in Scotland.
A Conservative source said: “Hunting is a devolved issue. The SNP’s decision to vote on a draft law that does not affect Scotland at all shows exactly why Conservatives committed in our manifesto to ensure laws that only affect England can only be passed with the consent of English MPs.”
Anti-hunting campaigners had accused the government of trying to reintroduce fox hunting “by the back door”.
But hunting supporters backed the move, saying traditional hunting would remain illegal and it would make it easier to manage fox populations.