Tracy Brabin was due to take questions from elected members at next Wednesday's full council meeting.
But the council has now cancelled that meeting, citing rising Covid infections which are currently at their highest ever local rate.
The authority said the move would "help keep people safe", with the meeting chamber at Wakefield's County Hall offering relatively limited space for 63 members to social distance.
But senior Conservative and Liberal Democrat councillors have reacted angrily to the decision and called for the meeting to be reinstated "with immediate effect".
They also accused Labour of making a system "deliberately geared to avoid its operators being called to account".
In a letter sent to council leader Denise Jeffery and chief executive Andrew Balchin, they said: "It is with a considerable degree of dismay that we learn of the plan to cancel this month’s full meeting of the council, due to the claim that it cannot be conducted “safely”.
"Whilst in no way wishing to underplay the health risks which may be posed to a very small number of members by the Omicron Covid variant, this decision looks like it has been made, not on the grounds of safety, but merely on the basis of it being another convenient opportunity for the controlling group to avoid scrutiny, which in Wakefield is already woeful as it is.
"Our Westminster parliament with its 650 members is sitting daily in its very cramped and crowded debating chamber.
"Yet, in Wakefield, our chamber is considered too small to accommodate what is realistically, an absolute maximum of 70 people on well over 120 seats, once every month."
The letter was signed by Conservative and Lib Dem group leaders Nic Stansby and Tom Gordon, as well as their deputies, Tony Homewood and Adele Hayes.
The quartet also called on the council to "properly consult" with Opposition members before any further decisions over meetings are made.
The council has been contacted for comment in response to the letter.
The local authority had earlier made the announcement, while confirming other council meetings will be held online for the rest of January.
Chief legal officer Gillian Marshall said: "Due to rapidly rising case rates, we have taken the difficult decision to cancel next week’s meeting of full council in order to help keep people safe.
"Other public meetings due to take place this month will also be held virtually instead so they can continue to be watched by our residents, or postponed to a later date, and we shall review the situation at the end of this month."
By law, meetings which involve decision-making must be held in person, after emergency legislation allowing councils to hold them virtually expired last May.
Ms Marshall said the council was "continuing to lobby government" to change that position.
Police numbers and rising crime were among the issues Mayor Brabin would likely have faced next week, with councillors across the political spectrum raising concerns about the lack of bobbies on the beat.
Policing now forms part of Mayor Brabin's remit, after her role was merged with that of the Police and Crime Commissioner upon her election.
Local Democracy Reporting Service