The Gunners manager also provided updates on William Saliba and Ezri Konsa, discussed Declan Rice's development and explained why he was delighted with Viktor Gyökeres' recent performances.
Saka is expected to begin increasing his on-pitch activity after the international break, but Arteta was reluctant to put a target date on the winger's return.
"We're talking about obviously weeks. Let's see, after the international break, he's going to start hitting the pitch and start to have more activities, how he feels, but unfortunately he's going to be out for a while.
"I don't want to put these guys under too much pressure, they are doing their best to get in shape. Bukayo is desperate to get back with the team, but he's still quite far away."
The absence of Saka did not prevent Arsenal from having a strong presence in Thomas Tuchel's latest England selection, with five players called up. Arteta said having a substantial English contingent was an important part of the club's identity.
"It's a proud thing, obviously, to have a big English core in the national team, our club, it's something that is part of our identity, not only the number but the players that represent us and the national team. They are super happy to be back, you can see that."
Ben White was among those recalled, having impressed Arteta with his performances this season. The manager was pleased to see the defender rewarded after his previous history with the national team.
"He's been brilliant and I'm really happy with that. We know the history behind what happened with Ben, he looked really happy and it's a moment that he's earned it and he needs to enjoy now."
Saliba and Konsa provide defensive encouragement
There was also positive news regarding Saliba, who had returned to training after his recent absence. France were due to announce their squad later in the day, and Arteta confirmed the club had been in close contact with the national team.
The Arsenal manager acknowledged that Saliba needs minutes and understands the defender's desire to represent his country, leaving the final decision to France coach Zinedine Zidane.
Ezri Konsa, meanwhile, was feeling much better after being withdrawn as a precaution following the Champions League victory over Slavia Prague.
"Yeah he's fine, he was feeling much better today, we took him out for precaution and for the amount of minutes that he was playing but yesterday and today he's feeling good."
Rice and Gyökeres impress Arteta
Arteta was particularly enthusiastic when discussing Rice's development. The midfielder has added greater attacking threat to his game, registering five Premier League assists and scoring against Bayern Munich.
"The mentality to go out and win football matches and to add another level to his game, another kind of threat and be much more unpredictable, and we've been working a lot on that.
"He's desperate to improve every part of his game, and we need to do that while we maintain so many incredible things that he's already done, but he's on the right trajectory."
Gyökeres also earned praise after an impressive week, with Arteta highlighting not only the striker's goals but the confidence and energy he brought to the side.
"Very good, I think everybody was so happy to see, not only the goals, I think his overall performance, how free he looked, how happy he looked, the energy that he could transmit on that football pitch.
"That's exactly what we need, that's what we're signing, that's the type of player that can help us to make the difference and he certainly did that tonight."
Arteta also made clear that Arsenal would approach Hull with the intention of maintaining their momentum before the international break. He praised the job done by manager Sergej Jakirović and the club, saying their performances after promotion had been impressive.
The immediate focus, however, was on securing another victory and carrying their form into a demanding period of the season.