Arteta's comments come after Pierre-Emerick Aubameyang was removed as captain last week following a disciplinary breach.
Aubameyang, who signed a new three-year contract with the club last year, was dropped ahead of this month's 2-0 win over West Ham United after he returned late from a trip abroad.
"I do not establish my authority by being dictatorial or ruthless," Arteta said in comments published by British media on Thursday.
"I just ask for one thing – respect and commitment. At this level, if I don't get that, I'll pack my bags and go somewhere else because that's the minimum I can ask for.
"To be successful you have to be passionate about something and, if you want to represent a club of this size, that is the minimum standard you have to bring.
"I am not going to ask anybody to put the ball into the top corner every time they hit it, but I will ask them to do the right things every single day for this club."
Arsenal, fourth in the Premier League, take on bottom side Norwich City at Carrow Road on Sunday.