Celtic revealed the incident happened during the second half of the Absa Premiership tie, with a motive for the attack yet to be established.
Phunya Sele Sele said they are now considering moving their games away from Botshabelo.
A statement on the club's official website said: 'Bloemfontein Celtic supporters and management should be celebrating the 5-1 nil against Polokwane City but the team is disturbed by the unruly behaviour that was displayed in the stands by criminal acts during the match.
'In an altercation that took place in the second half, three supporters residing in Bloemfontein were stabbed for no apparent reason. William Lenong of Joe Slove was stabbed in the thigh while Ishmael Reeman of Heidedal was knifed in the stomach and on the back. Both supporters have been released from hospital except for Tiisetso Tlali of Cape Stand.
'The team’s management has responded to the medical needs of the supporters and has visited them in hospital. A case has been opened against the perpetrator who is under the watchful eye of the police.
'Celtic apologises to fans that witnessed the attack and will take every possible action to ensure the safety of its supporters.
'Although the motive for the attack has not been established, gang related violence can’t be ruled out. Celtic is evaluating the possibility of moving matches away from Botshabelo which is rife with rival gangs.
'Bloemfontein Celtic thanks the medical team that attended to the supporters and the police that apprehended the suspect. Community members are encourage to assist the police with their investigations.
'Anyone with information and input that can help the police and the team can contact the Bloemfontein Celtic liaison officer, Pule Malebo on 063 060 1619.'
Celtic's managing director Rali Ramabodu said: “We are disturbed by this barbaric act which was also seen by youngsters in the stands. We have worked hard to create family environment at our games.
“Any type of violence my deter fans from attending games and can lessen kids’ interest in attending games. We encourage our supporters to report any unruly behaviour and appeal to them to continue coming to our games.”