The £840m QEUH campus, which includes the Royal Hospital for Children, was hailed as a world leading facility when it opened in 2015.
However, it has been dogged by infection outbreaks and concerns around the water and ventilation systems.
Such issues are being investigated as part of the Scottish Hospitals Inquiry.
The Scottish government said it was “deeply concerned” by the cremation incident.
A spokesperson said: “We wish to express our sincere condolences to the families involved with this terrible incident.
“We have been clear with NHS Greater Glasgow and Clyde that they must fully investigate the circumstances.
“We will also carefully consider the findings of the senior inspector of burial, cremation and funeral directors into the circumstances.”
