The Gunners brought their record goalscorer back to the Emirates in January to provide cover during the Africa Cup of Nations.
Henry, 34, has scored two goals in his five appearances and is due to return to the MLS on February 17.
Gareth Southgate will take charge of the England team for the remaining four matches of 2016.
Gareth Southgate has been placed in charge of England for their next four games after Sam Allardyce left by mutual
Celtic face another massive task in the Champions League when they welcome Manchester City to Parkhead on Wednesday night.
Following the departure of England manager Sam Allardyce, Under-21s coach Gareth Southgate is set to charge of the senior team
The latest gossip and rumours from the newspapers:The Daily Echo reports that Southampton defender JOSE FONTE, linked with a move
The shock ending to Sam Allardyce's ill-fated England reign has left the national team without a manager just days before