Bercow said a motion on the deal had already been brought before MPs on Saturday, and it would be "repetitive and disorderly" to debate it again, the BBC reported.
Saturday's sitting saw an amended motion nodded through by MPs, withholding approval of Prime Minister Boris Johnson's deal until it has been passed into law.
Johnson's spokesman said he was "disappointed" by the decision.
He added: "The Speaker has yet again denied us a chance to deliver on the will of British people."
The UK is due to leave the EU in 10 days, and while Johnson and fellow EU leaders have agreed to a new deal to allow that to happen, it cannot come into force until it is approved by both the UK and European parliaments.
The government wanted to hold a "yes" or "no" vote - or so-called "meaningful vote" - on its deal on Saturday, but MPs instead chose to back an amendment tabled by former Tory Oliver Letwin, which said that could not happen until legislation, called the Withdrawal Agreement Bill (WAB), was passed.
The WAB will be introduced later, but will then have to go through full parliamentary scrutiny in both the Commons and the Lords.
No. 10 was pushing for a second shot at a meaningful vote on Monday, but Bercow told the Commons he would not allow it, and had come to that decision on the basis of a parliamentary convention dating back to 1604.
He cited Parliament's rulebook which says a motion that is the same "in substance" as a previous one cannot be brought back to the Commons during the course of a single parliamentary session.
The Speaker also said the circumstances around the motion had not changed, so his ruling was "necessary... to ensure the sensible use of the House's time and proper respect for the decisions that it takes".
But Tory MP and Brexiteer Sir Bernard Jenkin appeared to accused Bercow of bias, saying it was "remarkable" how often the Speaker "pleased one lot and not the other".
"It is most unusual for a Speaker so often to prevent the government having a debate on the matters which the government wish put before the House," he added.
Fellow Tory David TC Davies said: "The only consistency one can find in your rulings is that they always seem to favour one side of the argument and never the government."
But Bercow disagreed, adding: "The consistent thread is I try to do what I think is right by the House of Commons."
( With inputs from IANS )