An SNP source said: “This has come as a huge shock to the party. As there are live criminal proceedings, we can’t comment any further at this time.”
Deputy leader Eric Drysdale will step in as acting leader until the next full council meeting on 29 October.
Councillor Drysdale told the Local Democracy Reporting Service: “I acknowledge the resignation of Grant Laing as leader of Perth and Kinross Council following today’s developments.
“These are very serious matters and it is right that due process takes its course.
“In the meantime, my priority as acting leader is to ensure stability and continuity for the council, its staff, and the communities we serve. We will continue to focus on delivering essential services and supporting the people of Perth and Kinross.”
Laing’s resignation was announced earlier in a brief update on the council’s website, external.
The council declined to comment further.
The SNP has confirmed to the BBC that Laing is no longer a member.