Arteta took over from Unai Emery in December 2019 and his previous deal was set to expire at the end of next season.
Arsenal got off the mark when Eddie Nketiah pounced on a weak back pass by Christensen before slotting past goalkeeper Edouard Mendy in the 13th minute.
The Egyptian midfielder has been linked with a move away from the Gunners as Turkish giants, Galatasaray, showed interest in signing the player.
The Pharaohs pulled out a sensational comeback against Angola on Friday night to book their place in the final round of the World Cup qualifiers.
The miserable run of results is despite the fact the club were the biggest spenders in the summer transfer window.
Elneny's injury forced him to miss Egypt's 1-1 draw with Gabon in the African World Cup qualifiers last Sunday.
Arsenal sent a medical report of the player's injury to the Egyptian Football Association (EFA), which revealed that the player is injured and will not be fit for Sunday's game in Liberville.
The duo missed Egypt's opening game in the qualifications against Angola on Wednesday as their clubs refused to release them.
Egypt will travel to Liberville to face Gabon on Sunday and the Egyptian fans hope to see a more beautiful performance from the Pharaohs.
During his five years at the club, Elneny has made 130 appearances for the club, including 69 games in the Premier League.
Alexandre Lacazette struck twice, including a penalty, while Nicolas Pepe and Bukayo Saka also found the net in the quarter-final second leg to set up a last-four clash with Villarreal.
Arteta called on his players to "create magical moments" in Thursday's Europa League quarter-final second leg against Slavia Prague.
Arsenal host champions Liverpool on April 3 after the international break.
Egypt faces Kenya on Thursday in Matchday 5 of the Africa Cup of Nations qualifiers.
The English giants advanced to the second round with a 100% record as they won their six group stage matches.
oe Willock and Nicolas Pepe gave Arsenal a comfortable 3-0 Europa League win over Irish side Dundalk.
The Gunners aim to bounce back after their poor results in the league, having lost the last two matches to Manchester City and Leicester City.
The two players were included in Arteta’s squad for the Europa League.
Elneny has been an important player for the Gunners under Arteta's command.
The Egyptian midfielder joined Besiktas from Arsenal last summer on a season-long loan deal and since then he became a vital member at the club.