The prime minister is continuing to face pressure from her own MPs to resign following her pledge of a “new deal” on Brexit.
This comes after Commons Leader Andrea Leadsom left her Cabinet job in anger over Ms May’s Brexit plan. Andrea Leadsom resigned, saying she no longer believes the Government’s approach will deliver on the referendum result to leave the European Union.
Downing Street has announced she will be replaced by Treasury minister Mel Stride.
Several cabinet ministers have told the BBC that Mrs May cannot stay in her post.
Theresa May had told the commons that the legislation would be published on Friday.
But, standing in for Mrs Leadsom on Thursday, Mark Spencer told the Commons: “We will update the House on the publication and introduction of the Withdrawal Agreement Bill on our return from the Whitsun recess.”
He added that the government planned to publish the bill in the first week of June.
“We had hoped to hold second reading on Friday 7 June,” he added.
“At the moment, we have not secured agreement to this in the usual channels. Of course we will update the House when we return from recess.”
Second reading is when MPs get a first chance to debate legislation, before deciding whether it should proceed to detailed scrutiny.