Toure had been struggling with a thigh problem and missed Saturday's victory over Aberdeen but the absence of Simunovic is a major surprise.
The Croatian kept his fourth clean sheet in a row after coming in alongside Erik Sviatchenko for the 1-0 Ladbrokes Premiership win at Pittodrie.
Manager Brendan Rodgers indicated after the game that the pair would be his regular partnership but assistant Chris Davies has said that the 22-year-old would not be risked in a second game in four days after returning from an eight-month knee injury lay-off in September.
Griffiths is ill while Celtic were already without left-back Kieran Tierney, who suffered an ankle injury in training last week.
Davies, quoted on Celtic's official website, said: "Leigh Griffiths is not very well
He wasn't at training so he won't be travelling out.
"Jozo Simunovic is building up his progression back into the team
He was out for a long time so he won't travel.
"Kolo Toure still has a slight issue and KT has his issue as well."
Eoghan O'Connell could now feature alongside Sviatchenko and Rodgers has the option of playing right-back Mikael Lustig in the centre with Cristian Gamboa able to come in.
Source : PA