Manvir Singh, 21, was last seen by his friend in Renfield Street, near to Sauchiehall Street, at around 4.45pm on Wednesday.
The Glasgow University lives in Linnhe Avenue, Bishopbriggs and his family are "increasingly concerned" about him.
Mr Singh is described as 5ft 10in, of slim build, with short black hair and a goatee beard.
When he was last seen, he was wearing a navy blue hooded top with yellow markings on it, dark coloured jeans and tan coloured boots.
He was carrying a black bag.
Sergeant Salvatore Schillaci said: "It is out of character for Manvir not to keep in contact with his family.
"They are becoming increasingly concerned for his safety.
"Manvir is a medical student at Glasgow University and extensive enquiries are ongoing in the Greater Glasgow area to trace him.
"I would also urge Manvir himself to contact his family or Police Scotland as soon as possible to confirm that he is safe and well."
Anyone with any information is asked to contact Police Scotland on 101.