International trade secretary Anne-Marie Trevelyan said instead, Johnson should be focusing on “important” prime ministerial matters.
It follows an extraordinary week in the House of Commons in which the government faced accusations of a return to “1990s sleaze culture”.
Last Thursday, Johnson was forced to u-turn over a controversial plan to prevent Tory MP Owen Paterson facing a 30-day commons suspension for a serious breach of lobbying rules. The row resulted in Paterson quitting as an MP.
The government is set to face another tough few days with further allegations of sleaze emerging in the Sunday papers.
Labour leader Sir Keir Starmer said that a no-show by the prime minister in Monday’s debate would demonstrate he was “either too arrogant or too cowardly to take responsibility” for the Paterson lobbying scandal.