The 22-year-old has been out of action with injury since the end of February, and it was thought that the England international would return to the matchday squad at the end of April.
However, it has now been confirmed that the midfielder has suffered a setback and is likely to be on the treatment table for the next six to eight weeks.
England manager Roy Hodgson will name his 23-man squad for this summer's European Championships on May 12, but Oxlade-Chamberlain will not be included.
In Friday's press conference, Wenger told reporters: "There is no chance of the Euros for him. He will be back at the beginning of July."
Oxlade-Chamberlain has been linked with a move away from Arsenal this summer, with Southampton and Manchester United being rumoured as potential suitors.