The centre-back served an automatic ban in the 3-1 first-leg victory at Celtic Park on Wednesday after being sent off against FC Alashkert in the previous round.
However, UEFA's control, ethics and disciplinary body (CEDB) has decided that Simunovic's high challenge on Brazilian midfielder Jefferson warranted further punishment.
"The CEDB has decided to suspend the Celtic player Simunovic Jozo for two UEFA competition matches," the governing body wrote in a statement.
"The player has already served one match and will therefore be suspended for the next match for which he would be otherwise eligible."
The winner of the tie, which concludes in Norway on August 1, faces AEK Athens in the third qualifying round.