The Parkhead side flew out to Denmark on Monday ahead of the fixture. on Wednesday with the score 1-1.
Griffiths wasn’t part of the travelling party.
The Scottish Sun reports he suffered a calf injury in training on Monday before the flight with the decision taken to leave him behind.
The 30-year-old was brought off the bench to some boos on Saturday in the friendly defeat to West Ham United at Parkhead.
Celtic will be reliant on Odsonne Edouard to fire the club into the third round where they will likely meet Dutch giants PSV.
The Frenchman has been strongly linked with a move to Brighton & Hove Albion. Reports suggest the Premier League side have been weighing up a £20million offer.
However, according to local press in Brighton the Seagulls are not interested in the 23-year-old.