Hibs confirmed the 22-year-old had been involved in an incident involving the police and Fenlon admitted he had to think about whether to start the on-loan Wolves striker in the Clydesdale Bank Premier League clash at Pittodrie.
Fenlon said: "I wanted him to play today and he did okay, although he didn't really get a lot of service.
"You always think about decisions; who you're going to play and how it'll affect the game, and that was no different with Leigh today."
Reports emerged on Saturday that Griffiths had been detained over an incident in a Tesco store in Corstorphine, Edinburgh, but Lothian and Borders Police would not give any details about the identity of the arrested man.
A police spokesman said: "A 22-year-old man has been arrested and charged in connection with an alleged shoplifting incident in the Tesco store at Meadow Place, Edinburgh, on Saturday January 26. He will appear in court at a later date."
Hibs made a short statement on the matter. A spokesman said: "The club is aware of an alleged incident which took place on Saturday afternoon involving the player. This is now a police matter."
Griffiths was said to have denied that he had been caught shoplifting on his Twitter account, which is now protected from the public.
Earlier this month, Hibs said they would take disciplinary action against the player following a tweet that was criticised by anti-racism campaigners.