He did have an injury, but he has also played some. He just hasn't been particularly good in the minutes he has been given this season, before or after the injury. This is something that was already starting at the tail end of last season when he himself admits he was quite poor in a number of the games at the business end of the season.
Following the World Cup, he redeemed himself after a slow first year and slow start to last season, but he seems to be in a funk at the moment. The biggest gripe right now is that he seems short of confidence and he does not even try, let alone succeed at beating a man. End product and incisiveness are not there, but he's never been particularly outstanding in this regard at City and his control of the ball and drawing of fouls were deemed sufficiently valuable in that good stretch last season. He's seems to be playing rather safely and predictably and is thus easier to defend. His shots get blocked a lot and he's not posing much of a threat down the line, so defenders can anticipate his actions and contain him more easily.
Patience is starting to wear though, especially with the introduction of Doku, who has been beating defenders in his sleep and even chipping in with goals and assists, which were supposed to be a weakness of his. Having Doku come in and do this has brought Jack's deficiencies into further relief. Now, he and Doku are different players and bring different things to the team, but there is a bit of added pressure and visibility now because City have been drab and toothless at times without KdB this season.
All of this notwithstanding, I thought he would still start against Arsenal because I thought it would be a battle for control and that is what he brings. That he did not even play, with Doku also starting on the bench, may be a sign of his standing right now. Still, like people have said he did have an injury and the season is young. I would start to worry if it's the same stuff in a month or two.