The men, aged 23 and 27, were on a bridge between Durham Street and Cullingtree Road in the Westlink area of the city when they were attacked by an armed man at about 07:00 GMT.
Their injuries are not thought to be life-threatening.
Police have asked for anyone with information about the attack to contact them on the emergency number 101.
Two men have been treated in hospital for stab wounds after an attack in Belfast on Saturday.