Saka, who came through Arsenal's youth ranks, has been in top form for the London club this season with 12 goals and 10 assists in the Premier League as they lead the points table.
The 21-year-old also stole the limelight for England during the international break, scoring a goal and setting up another in their 2-0 victory over Ukraine in the Euro 2024 qualifying Group C at Wembley.
"He's going to have to deal with expectations of the media, with attention on the pitch," Arteta told reporters on Friday, a day before Arsenal host Leeds United.
"When you want to fulfil a role like the one he has at the moment, you need to be capable of doing that. So don't read too much, don't listen too much, just focus on what you have to do every day. That's it.
"And we always have a stick ready, don't worry."
Saka has bounced back brilliantly from missing a decisive penalty in the shootout in the Euro 2020 final and is tipped to be a serious rival to Manchester City's Erling Haaland for the Player of the Season award.
"He still has a lot of things to improve and a lot of things to maintain," Arteta added. "Before he wasn't able to do that. So he needs to continue to maintain those things and elevate the level of other things that he can still do better."
League leaders Arsenal have 69 points after 28 games, eight points more than second-placed City who have a game in hand.
