Union leaders are investigating a problem with supplies of baby blankets at the Princess Royal Maternity hospital.
Babies are wrapped in a towel straight after birth and later wrapped in blankets to maintain a healthy temperature.
Newborn babies can lose a lot of heat very quickly.
NHS Greater Glasgow and Clyde said there was a clear process for staff to obtain additional linen stocks if required but admitted shortages could affect individual wards.
The Royal College of Midwives said it was investigating the issue and suggested it could be linked to problems with the laundry system.
Gillian Smith, director of Royal College of Midwives in Scotland added: "The most important thing is that the baby is kept warm. Obviously a blanket is softer than a towel."
In March the Evening Times prompted a parliamentary investigation after we revealed patients were facing a shortage of blankets at the Royal Alexandra hospital in Paisley.
First Minister Alex Salmon was forced to issue an apology and promised an investigation after meeting patients who were told hospital blankets were like "gold dust".
The health board cited "internal operational issues" for the shortage.
A spokeswoman for NHS Greater Glasgow and Clyde said: "Babies born at the Princess Royal Maternity are normally wrapped in towels immediately following their birth.
"They remain wrapped in a towel on transfer to the postnatal ward. When they are given their first bath they are then clothed and wrapped in a baby wrap. Layers of blankets are added as necessary.
"However, there may be occasions when linen stocks in individual wards are depleted and fresh supplies are awaited. On those occasions staff may wrap a baby in a towel until fresh supplies are delivered."
Scottish Labour's Shadow Health Secretary Jackie Baillie, left, said: "These are deeply disturbing revelations and expectant mothers will be understandably concerned.
"These are basic provisions that anybody should expect in hospital.
"Nicola Sturgeon is meant to be in charge of health in this country – she needs to step in and sort this out urgently."