The retired football manager toured the Southern General Hospital today in his role as a Unicef ambassador.
The charity is working with Glasgow 2014 to promote its baby friendly initiative across all Commonwealth nations, which aims to improve health and reduce disease, poverty and exploitation among children.
Sir Alex met new mother Rebecca Young and her twin boys Elliot and Sandy, plus nurses at the hospital to see how they support new families.
The 72-year-old also met Kimberley Black, who has spent the last week in the hospital's neonatal unit with her 12-day-old son Jason.
Sir Alex said: "I've been privileged to see the life-changing work that Unicef does to help children around the world, but I wasn't fully aware of the vital work that is done here in Glasgow and across the UK.
"As a father and grandfather, I value strong family relationships. Seeing this level of expertise at this hospital emphasises to me how important it is for mothers to have the vital support they need to help nurture their children and give them the best start in life."