The victim was with a friend in McKechnie Street, Govan, when the attack took place at about 11:10 on Wednesday.
He was taken to South Glasgow University Hospital and treated for a serious facial injury before being allowed home.
His attacker is described as a white male in his 20s, with light brown hair.
Police Scotland, who have appealed for witnesses, said the suspect ran off towards Harmony Row.
Det Con Adam Richardson, of Govan CID, said: "We are currently studying CCTV footage in an attempt to get a clearer description of the person responsible for this vicious attack.
"At this time there is no apparent motive for the attack and I appeal to anyone who either witnessed the incident or who saw the suspect running off afterwards to contact police immediately."
A 61-year-old man was slashed in the face after being attacked from behind as he walked along a Glasgow street.