CCTV images show Michael Slaven, from Dumbarton, outside the Glasgow's St Enoch subway station at around 2am on Friday.
The 23-year-old electrician had been out with a group of friends but left the Sugar Cube nightclub in Queen Street alone.
He did not return to the home he shares with his mother Elaine, 53, and siblings in the West Dunbartonshire town.
Police officers are scouring the footage and carrying out "extensive enquiries" into the disappearance, said to be highly unusual.
His father John Slaven, 52, said: "This is not like Michael because he hasn't used his bank card or phone since he went missing.
"He calls his mum to let her know where he is all the time so we have no idea what's happened to him.
"He's very sociable person but likes his home comforts and never goes on benders.
"He seemed to be acting a bit odd on the CCTV pictures so if anyone saw him or knows where he is we would ask that they get in touch."
Michael was last seen wearing a white T-shirt with a printed photo on the front, and light green jeans.
A Police Scotland spokesman said: "A team of dedicated officers are carrying out enquires and have been liaising with Mr Slavin's family on a regular basis."