People have been asked not to arrive early for appointments, and the health board said those having to queue would be provided with water and mobility support if needed.
It comes after reports of long queues each day this week, with people waiting up to two hours for their appointments.
The health board staff bank put out an urgent call for staff on Thursday in the face of “extreme” staffing shortages on Friday.
This week, NHS Greater Glasgow and Clyde said queues have formed because clinics are adapting to a new model of vaccination, with three vaccines now on offer: Pfizer, AstraZeneca and Moderna.
A spokesperson said: “Starting this week we began vaccinating those under 30 years and coupled with the accelerated second dose programme, we are seeing very high uptake across centres, including the Hydro.
“As a result of the increased rollout, we are now managing and administering three different types of vaccine at the SSE hydro and other clinics which is a complex process.
"While our clinics adapt to the new model, our staff are working as hard as possible to minimise queuing times, and we apologise to any patient who has had to wait longer than expected.
“We are ensuring people are made aware of potential waiting times, provided with water and if required, support with mobility. We would also ask the public to ensure they turn up at their allocated appointment time to help us manage numbers more efficiently.”
Some 76 per cent of adults in the Greater Glasgow and Clyde health board area have received a first dose of vaccine, while 47.4 per cent have had both doses.
The Scottish Government said there is no shortage of vaccinators across Scotland.
Recent staffing shortages reported in Glasgow, and prior to that Lanarkshire and Lothian, were caused by a “temporary compression of the programme”, a spokesperson said, as a result of the decision to shorten the gap between first and second doses from 12 to eight weeks.
NHS Lanarkshire and NHS Lothian requested extra vaccinators from the Armed Forces to cope with this added pressure, but NHS Greater Glasgow and Clyde did not.
The spokesperson said: "All health boards were asked to have enough workforce capacity to deliver our key vaccination milestones, which we are on course to meet. This has been achieved according to each board’s population share. In the event of a health board requiring additional capacity to deliver more vaccine, then consideration is given to requesting military support.
“Revised JCVI guidance to shorten the time between doses led to a temporary compression of the programme. NHS Lothian and Lanarkshire both requested military support to provide additional vaccination capacity and this was agreed between MOD and the Scottish Government. NHS Greater Glasgow and Clyde did not require such assistance.”