According to the Scottish Sun, Griffiths injured his calf in training on Monday before the journey, prompting the decision to leave him behind.
Celtic manager Ange Postecoglou will be without Leigh Griffiths for the second leg of their Champions League qualifying tie against FC Midtjylland.
In Saturday’s friendly loss to the Hammers at Parkhead, the 30-year-old was introduced from the bench to some boos.
The Hoops will rely on Odsonne Edouard to help them through to the third round, where they will most likely face PSV.
The transfer to Brighton & Hove Albion has been heavily linked with the Frenchman. According to reports, the Premier League club has been considering a £20 million bid.
The Seagulls, though, are not keen to sign the 23-year-old, according to local media outlet in Brighton.