Emergency services were called to the station on Stockwell Road on Wednesday just before 3pm after reports of the stabbing.
A man has been arrested on suspicion of grievous bodily harm. Paramedics took two men to local hospitals for treatment.
“Their injuries are not deemed life-threatening or life-changing,” British Transport Police said in a statement.
“Enquiries into this incident are ongoing and platform one remains closed while officers attend.”
The Victoria Line was suspended between Victoria and Brixton has now reopened.
Transport for London (TfL) said earlier: “No service between Victoria and Brixton due to a customer incident at Stockwell. Tickets are being accepted on London Buses and South Eastern Trains (Victoria - Brixton), South Western Railways (Vauxhall - Waterloo) and London Overground and Greater Anglia (Liverpool Street to Tottenham Hale).”
There are minor delays on the rest of the line.
Witnesses, or anyone with information, can contact BTP by texting 61016 or calling 0800 40 50 40 quoting reference 341 of 23 November.