The Brazilian centre-half came off during the team's 1-0 home loss to Leicester City on Sunday night in the Premier League.
The Gunners put in a lacklustre display and were out done on the counter, after Luiz had been substituted.
Asked by reporters about the injury, Arteta had few words.
He said: "I don't know. We've lost a few players in the last week or so.
"David had a muscular problem and he couldn't carry on - we'll have to assess him in the next 48 hours."