Spurs experienced a disastrous first half at the Tottenham Hotspur Stadium, conceding a 15th-minute opener before Micky van de Ven saw his effort chalked off for an offside infringement.
Bukayo Saka then doubled Arsenal's advantage shortly before Werner was forced to make way due to an injury issue.
Kai Havertz added a third in the 38th minute to leave Ange Postecoglou's side with a mountain to climb in the second period.
Spurs attempted to mount a dramatic fightback as Cristian Romero took advantage of a David Raya mistake to get his side on the board, before Son Heung-min scored an 87th-minute penalty to halve the deficit.
Werner could miss Chelsea reunionDespite their best efforts, Tottenham were unable to complete the comeback, ensuring that they fell to a second straight defeat.
As well as reflecting on a disappointing result, Postecoglou will also have concerns about the extent of Werner's injury issue.
The 28-year-old saw his fifth consecutive start curtailed by an apparent muscle injury, resulting in him being replaced by Brennan Johnson in the 31st minute.
Werner, an RB Leipzig loanee, is now an obvious doubt for Thursday's Premier League fixture against his former club Chelsea.
Tottenham will also have to wait to find out whether Werner will be available for their four other fixtures against Liverpool, Burnley, Manchester City and Sheffield United.
Has Werner played his last game for Tottenham?While Spurs will hope to have Werner back as soon as possible, there is a possibility that the German attacker has played his final game for the club.
As it stands, Werner is set to return to Leipzig at the end
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