Ozil has not travelled with the squad for the side's Europa League game at Eintracht Frankfurt.
Johnson told talkSPORT: "When players are rested, they can be rested on the bench.
“So they can miss 80 minutes but they can travel with the squad, sit on the bench. But you're still part of the plans, there to support the lads, needed in maybe the last 10 minutes.
“The fact he's not travelled at all tells me it's not about rest, there's definitely more to it than that."
“You don't normally just leave players - certainly not the big players - at home," Johnson added. “Especially if he's going into training or training on his own with five young kids - nobody wants to do that.
“It's frustrating to not travel with the team, for one. And then it's frustrating to train on your own when your team-mates are having a game. Not many players would accept that anyway.
“The reasons Ozil's apparently retired through international football is through getting a bit of stick and this and that.
“He's become a top, top player and you can't get there and have the career he has had without getting stick off someone along the line. I'm a big fan of him as a player but I do question what goes on between the ears.
“I don't think they want him there. He's on too much money so he's hard to get out, he know's he's on too much money to get out, so the ball's in his court.
“Somehow, whether it's him and the manager or him and the club or all three, someone's banging their heads together."