Dominic Heslop, who represents the Pentland Hills ward, said it was “outrageous” that the council was carrying on with business while the funeral of the former prime minister was taking place.
He said he had tried to persuade Conservative MSPs to take a similar stance at the Scottish Parliament.
The council’s development management sub-committee, which decides planning applications, was going ahead in its normal Wednesday morning slot.
However, Councillor Heslop sent a note to the committee clerk saying: “Please can you accept my apologies for this meeting. I do not believe that any council, or indeed parliamentary business, should take place tomorrow when we are laying to rest our greatest prime minister since Churchill.”
He will not be present while the committee discusses developments including plans to build 32 townhouses on Ocean Drive, listen to a report on plans by developer Cala for a residential development at Craigpark Quarry outside Ratho and vote on an application to build colony homes at Albion Road.
Cameron Rose, Tory group leader on the council, is also on the development management sub-committee, but will be in London for the funeral along with other leading Conservatives from the Capital.
Cllr Heslop said: “I am boycotting the meeting as a matter of principle and I have e-mailed John Lamont, our whip at the Scottish Parliament, to see if he can boycott business there as well.
“I certainly believe there should be no business conducted when the funeral is taking place. I would much rather be part of the funeral, whether watching on TV or being there in person, rather than in some planning committee I believe should have been cancelled.”
Planning convener Ian Perry said: “As far as I’m aware we have had no formal request from the Conservative Party to cancel any meetings. If Dominic wants to miss the meeting because of the funeral that’s his right as an individual councillor to do that.”
Cllr Heslop’s protest came as MSPs prepared for a debate on public procurement in place of the proposed session on the theme “There is still such a thing as society”.