The 27-year-old has been a cornerstone of Arsenal's defence this season, forming a formidable partnership with Frenchman William Saliba.
Their pairing has seen the Gunners concede just five goals in 11 Premier League matches, a record that has propelled them to the top of the table, four points clear of second-placed Manchester City.
Gabriel's absence is a setback, particularly given his aerial threat from set-pieces, but Arsenal have several options to cover, including close-season signings Cristhian Mosquera and Piero Hincapie.
"Gabi unfortunately picked up an injury with the national team. He will be out for weeks," Arteta told reporters on Friday. "We need to have another scan next Wednesday. We will have the timeline much more clearly than we have at the moment.
"It's clearly a blow. It's our leader in our backline. To miss him is never a positive thing. The good thing is we have some very good options. They need to stand up now."
Defender Riccardo Calafiori has yet to train, having withdrawn from the Italy squad with a hip problem. Arteta remained tight-lipped about the 23-year-old's availability for the clash at the Emirates.
"He missed the (Italy) games. He wasn't available. He's been carrying a few things. We had to bring him back. He hasn't trained yet. We have another session tomorrow. Let's see," the Spaniard said.
Arteta did not say whether any other players who have been out injured - including Martin Odegaard, Kai Havertz, Gabriel Martinelli, Noni Madueke and Gabriel Jesus - would return against Spurs.
"We put a lot of energy in the international break with the medical staff to try to bring them back as quickly as possible ... I'm hopeful we can make a step tomorrow. But certainly? I cannot tell you," Arteta said.
"I think they're going to be with us soon. But I don't know if Sunday is too soon."
'Clear identity'
Arteta praised Spurs manager Thomas Frank, who took over in June following the dismissal of Ange Postecoglou.
Spurs sit fifth with 18 points, eight fewer than Arsenal, a significant improvement from their 17th-place finish last season.
"Thomas has brought something very different to what they had before, and the remarkable job he did at his previous club (Brentford)," Arteta said. "He's given a clear identity to the team — how they want to play and compete. It's going to be very tough."
Arsenal's Eberechi Eze will be the focus of attention on Sunday, as the England winger prepares for his first North London derby. The 27‑year‑old was at the centre of a transfer battle in the summer, ultimately rejecting Spurs to join their rivals from Crystal Palace.
Spurs, forced to look elsewhere after missing out on Eze, responded by signing 22‑year‑old Dutch playmaker Xavi Simons from RB Leipzig.
"Ebz had many offers to go to different places. He was allowed to leave and he chose to come here which I'm very proud of. It's going to be a game I can't wait for him to experience, because he's very special," Arteta said.