The England international, who was due to start, suffered a hip problem and was replaced at kickoff by Noni Madueke.
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With crucial fixtures against Chelsea and Sunderland looming, Arteta hopes to have his key winger back soon.
Despite title rivals having a game in hand and upcoming matches on Sunday, Arteta can take comfort from ending a three-game Premier League winless streak at a challenging venue.
“To win 4-0 here is very difficult, let's see when the next time that happens. Big credit to the boys,” Arteta told BBC Match of the Day.
“The team showed a real dominance, resilience and character and obviously quality. I really liked the attitude of the team.
“We don't know yet. He had a little niggle in the warm-up.”