The unprecedented move, which affects 15 sites in Glasgow and surrounding areas, follows separate 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.
Last month a 27-year-old woman suffocated at Dykebar Hospital in Paisley, two years after a patient committed suicide in similar circumstances at Stobhill Hospital, Glasgow. Neither individual has been named.
The Dykebar probe centres on how the patient was able to take her own life despite being constantly monitored. 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 use of the bags from yesterday at 15 mental health hospitals and inpatient services under the board's jurisdiction.
However, NHSGGC complied with the unprecedented request before it could be enforced.
The ban on bin bags is unusual according to the HSE spokeswoman, and has not been extended to other NHS boards in Scotland.
A spokeswoman confirmed it was examining the circumstances surrounding both deaths, saying: "HSE is investigating the deaths of two patients on mental health wards at Stobhill and Dykebar Hospitals. As part of those investigations we have asked NHSGGC to remove all plastic bin liners from mental health wards by Wednesday, April 16."
"A prohibition notice stopping the use of these bags would have come into force from midday, however, this did not prove necessary as NHSGGC took suitable action before the deadline."
The health board has already carried out a full investigation into the Stobhill death and has now also embarked on an internal critical incident review of the death at Dykebar. A spokeswoman said this was at an early stage.
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.
The spokeswoman added: "Our immediate actions have so far been focused on these two investigations.
"NHS boards in Scotland are responsible for managing their own risks to staff, patients and visitors and we would expect those operating mental health wards to manage those risks proportionately and in line with their own risk assessments and procedures. HSE will be contacting NHS Scotland officials to discuss appropriate standards across the board, and similar contacts will be made in England and Wales."
The Mental Welfare Commission, which aims to promote the rights and welfare of individuals with mental illness, would not comment on the deaths. Its chief executive, Colin McKay, said: "We receive notification from the hospital where a patient has died whilst receiving compulsory treatment under the Mental Health (Care and Treatment) (Scotland) Act 2003. Where the commission is notified of a death under these circumstances we will determine whether any further information is required or any action is to be taken."