The Ghana international, who moved to Arsenal from Atletico Madrid for €50 million during the summer, injured his thigh last month and only returned to the side on Sunday.
Partey pulled up injured shortly before half-time and was standing on the touchline when Spurs broke from their own box. Arteta then urged him back on to try to stop the counter-attack but the midfielder could only run a few yards before stopping.
Ahead of Partey, Spurs striker Harry Kane finished off Spurs' sweeping attack, handing the Premier League leaders their two-goal cushion.
"I was trying to push him but I don't think he realised the gravity of the situation when he left his position but that was probably because he was in a lot of pain," Arteta told reporters.
"Suddenly they are coming to attack us and Thomas is walking to me and I was trying to push him. I haven't spoken to him so I don't know exactly how it happened or if he felt something really serious."
Partey's absence will be a cause for concern for Arteta amid a busy schedule where Arsenal, 15th in the league, play eight games in 23 days.