According to Celtic's website, the supporter, who had travelled from Cape Town, was struck by a motorist close to Free State Stadium straight after the match ended 1-1 on Sunday afternoon.
"It is painful seeing anyone unceremoniously losing life in such a horrendous way," Tshabalala said.
"We are pained as the Celtic family, losing a supporter who has dedicated his life to Celtic, travelling thousands of kilometers just to watch his team.
"Our sincere and deepest condolences to the family. We will as a team visit the family of the deceased to try and see how we can possibly help. We request motorists to kindly consider the pedestrians at all times."
Phunya Sele Sele have urged anyone with information regarding the tragedy to contact the police.