It is understood the rate of conceptions plummeted to almost 0% over the past two months, alerting clinicians there was something seriously wrong.
Generally around 30% of women will become pregnant per cycle of IVF, with the Glasgow Royal Infirmary (GRI) unit typically performing above that national average.
Infertile couples who had been undergoing IVF at the artificial conception unit in the GRI are now being treated at the city's private Nuffield Hospital after NHS Greater Glasgow and Clyde (NHSGGC) observed a sudden decrease in the anticipated success rate.
The health board has so far been unable to identify what caused the decline in conceptions, but a full investigation has been launched and experts have ruled out a clinical explanation.
One possibility being looked into is that building works under way on the floor immediately above the unit, where clinical laboratories are being refurbished, may have disrupted or contaminated the artificial insemination process.
Around 25 NHS patients a week – including those who underwent treatment during the past two months – have been receiving IVF at the Nuffield's Assisted Conception Unit since November.
Until the mystery surrounding the alarming drop in conception rates is resolved, the Nuffield will carry out both the laboratory and surgery elements of IVF, although the GRI unit will continue to look after women coming in for check-ups or outpatient procedures.
Dr Helen Lyall, consultant gynaecologist at the GRI's Assisted Conception Service, said: "Assisted conception success is never guaranteed but we must make sure that every chance possible is given to every single one of our patients.
"Patients using our service should be assured that our decision to temporarily move activity to the Nuffield Hospital was a decision based on putting patients first while we look into what might be the reason for the reduction in our normal success rates."
David Snape, hospital director at Nuffield Glasgow, said: "We are delighted to be able to help our colleagues in the NHS at this time and we are particularly pleased that, with the collaboration of both teams, the GRI has been able to deliver a seamless service to all patients currently in the system."