The Hoops centre-back was given his marching orders for "serious foul play" after catching an opponent with a high boot in the goalless draw in Switzerland earlier this month.
Neil Lennon said after the match: "I’m not sure how much contact there really was, so it seemed a bit harsh in a pre-season friendly.
“Some [VAR decisions] go for you – we got the penalty from it, and I thought it was a penalty.
"But it is in the laws of the game, it is the referee’s interpretation, so you have to accept it and get on with it."
Match referee Fedayi San included the incident in his match report and the Swiss FA have subsequently filed a misconduct report to their Scottish counterparts.
Celtic were braced for Simunovic to face action and the 24-year-old - who has been a key man under Lennon - will now sit out the league opener against St Johnstone and the second game of the season at Motherwell.
The former Dinamo Zagreb defender will be free to face Nomme Kalju in the Champions League second qualifying round as the suspension only applies to domestic matches.
A statement from the Swiss FA read: "In accordance with JPP (Judicial Panel Protocol) Annex C, section 4, Part D paragraph 3, the misconduct reported shall be recorded and the resultant suspension applied.
"The outstanding suspension applied for this offence is two first team matches immediate (domestic football)."
His suspension will likely see summer signing Christopher Jullien, who joined from Toulouse for a reported fee of around £7 million, deputise in the backline alongside Kristoffer Ajer or Nir Bitton.