A shoulder injury picked up on Boxing Day against West Ham ruled the German out of Sunday's game against Newcastle and potentially the FA Cup clash with Tottenham.
The midfielder, who has started every Premier League game since his move from Real Madrid on the final day of the transfer window, hurt his shoulder during the 3-1 win over West Ham on Boxing Day.
Wenger told Sky Sports: "I would have loved him here [at Newcastle] but he had a shoulder problem, he fell on his shoulder. He will be out for two to three games."
The Germany international will not feature against Cardiff on New Year's Day and is a doubt for his side's FA Cup third-round tie against north London rival Tottenham but could make his return against Aston Villa on Jan. 13.
Jack Wilshere returned to the starting XI in Ozil's place at St. James's Park, joining Theo Walcott and Santi Cazorla in Wenger's attacking midfield trio.