Addai, who is the captain of Tema Youth, tried to clear a long ball in the 84th minute but ended up snapping his right leg.
The unfortunate injury caused a long stop in the game, which was played at the Madina AstroTurf Park.
The 19-year-old was subsequently substituted, but his side held on to record a narrow 1-0 win over Bibiani Gold Stars.
The Division One League Super Cup was created for the best performing clubs in the second tier of Ghana football.
The competition is being contested by newly-promoted Premier League sides Real Tamale United, Bibiani Gold Stars and Accra Lions as well as three second-placed teams.
These are Tano Bofoakwa, Skyy FC and Tema Youth, while the two third-best-placed teams Berekum Arsenals and FC Samartex 1996 join to make it an eight-club competition.
The tournament serves as a preparatory ground for the clubs ahead of 2021/22 season which will commence on October 29.