Reform UK leader Nigel Farage said he was “genuinely sorry” that Mr Yusuf had decided to stand down.
The Clacton MP added: “As I said just last week, he was a huge factor in our success on May 1st and is an enormously talented person.
“Politics can be a highly pressured and difficult game and Zia has clearly had enough. He is a loss to us and public life.”
Mr Yusuf earlier branded Ms Pochin’s question “dumb” as it was not Reform party policy.
He said: “Nothing to do with me. Had no idea about the question nor that it wasn’t policy. Busy with other stuff.
“I do think it’s dumb for a party to ask the PM if they would do something the party itself wouldn’t do.”
Ms Pochin had asked Sir Keir whether he would be joining countries including France, Denmark and Belgium in banning the face and body covering worn by some Muslim women.
She said: “Given the Prime Minister’s desire to strengthen strategic alignment with our European neighbours, will he in the interests of public safety follow the lead of France, Denmark, Belgium and others and ban the burka?”
Ms Pochin’s question triggered an outraged reaction from some MPs in the Commons, while the Prime Minister was visibly taken aback.
Sir Keir said: “Can I welcome her to her place, but I’m not going to follow her down that line.
“But now she is here and safely in her place, perhaps she could tell her new party leader that his latest plan to bet £80 billion of unfunded tax cuts, with no idea how he’s going to pay for it, is Liz Truss all over again.
“Although considering I think (Ms Pochin) was a Conservative member when Liz Truss was leader, she probably won’t.”