The Brazilian already has four goals and three assists in the Premier League for the Gunners, helping them to sit top of the table going into the international break after a superb start to the season.
However, Jesus has also picked up four yellow cards in the league, more than he got in the entire campaign in his last four seasons as a Manchester City player. No other Arsenal player has more than two.
The most recent of those came late on against Brentford for a trip, and it follows yellow cards against Bournemouth, Fulham and Manchester United.
It leaves Arteta with a problem heading into a crucial run of fixtures in October, with Tottenham and Liverpool the next two opponents once the Premier League resumes after the international break.
Players receive a one-match suspension if they pick up five yellow cards in the first 19 league games of the season, with ten bookings by the 32nd match resulting in a two-match ban.
That means Jesus is just one yellow card away from picking up a suspension, with it unlikely that he makes it through the rest of the first-half of the season without picking up another booking.
Should he be shown a yellow card in the north London derby, the Brazilian would then not be available when Liverpool travel to the Emirates a week later, in what would be a huge blow for the Gunners.
With Jesus so important to how Arsenal play, both on and off the ball, Arteta needs his striker to keep his discipline in the weeks ahead.