Edinburgh City Council said Mark Turley, Director of Services of Communities, has been sent home on full pay while the council conducts an internal investigation.
Mr Turley's wide-ranging remit covers involvement in the council's response to the baby ashes scandal at Mortonhall, the crematorium which secretly disposed of babies' remains without the knowledge of their bereaved parents.
Former Lord Advocate Dame Elish Angiolini's investigation into the scandal was revealed last week as damning.
The baby ashes scandal emerged in December 2012 when it emerged that the council-run crematorium had buried or scattered the ashes of babies for decades without their relatives' knowledge.
The families said they were told there would be nothing to scatter.
Mr Turley's remit also includes Liberton High School, where 12-year-old Keane Wallis-Bennett was killed last month when a changing room fell on her.
It was claimed concerns had been raised over the safety of the wall, and the Health and Safety Executive and police are investigating the tragedy.
One of the biggest fraud investigations at a Scottish council is still tackling problems related to two departments overseen by Mr Turley. That relates to claims homeowners were billed fake repairs and overcharged.
A council spokesman said: "The council's Director of Services of Communities, Mark Turley, has been suspended on full pay pending an internal investigation."