As a result, five people were detained for organizing the unauthorized Sunday parade, RIA Novosti reported Monday.
Sobyanin said he canceled the parade because of safety and traffic concerns. Police quickly dispersed Sunday's crowds.
The parade has been held annually since 1992.
The cancellation was proper "in view of the cold weather and the priority that is being given at present to resolving Moscow's traffic problems," said Irish Ambassador to Russia Philip McDonagh.
Moscow officials organized several other events to take the place of the parade, including a concert of Irish music.