The unprecedented move, which affects 15 sites in Glasgow and surrounding areas, follows tragedies involving the bags at two hospitals.
The board has been ordered by the Health and Safety Executive (HSE), which has been called in to investigate the deaths at the NHS Greater Glasgow and Clyde (NHSGGC) facilities.
One senior nursing source said: "This patient should have been seen and heard at all times. This is a serious lapse, but the HSE has been exceptionally quick to act."
The HSE's deferred prohibition order was to have banned the bags from yesterday at 15 mental health hospitals and inpatient services under the board's jurisdiction.
The ban on bin bags is unusual, the HSE spokeswoman said, and has not been extended to other NHS boards in Scotland.
A spokeswoman said: "HSE is investigating the deaths of two patients on mental health wards at Stobhill and Dykebar Hospitals.
"We have asked NHSGGC to remove all plastic bin liners from mental health wards by Wednesday, April 16."
She added that NHSGGC took action ahead of yesterday's noon deadline.
The health board has already carried out a full investigation into the Stobhill death and has begun an internal review into the death at Dykebar .
In a statement, the board added: "Following a full investigation into a tragic suicide in 2012 and a subsequent suicide in 2014, the HSE recommended the removal of small bin liners in our mental health wards.
"NHS Greater Glasgow and Clyde has fully complied with this recommendation. We would like to reiterate our deepest sympathies to the families of both these patients."
The HSE said the ban has not been extended to other boards because its immediate concern is investigating the two incidents. However, it will be contacting NHS Scotland officials to discuss appropriate safety standards across the board.