Alli was struck on the head by the projectile, with Spurs leading 2-0 in the 73rd minute of the Carabao Cup quarter-final at Emirates Stadium on Wednesday.
And Arsenal have now said sorry to Alli in a statement and suggested a lengthy ban could be in store for the offender, who they believe has been identified via CCTV footage.
"We have all been embarrassed by the individual who threw a bottle at Dele Alli during Wednesday night's match against Tottenham Hotspur," the Arsenal statement read.
"Behaviour of this type has no place at Emirates Stadium and after analysing CCTV footage, which showed him leaving the stadium after throwing the bottle, we have identified an image of the suspect. We are liaising with the Metropolitan Police and investigations continue in order to apprehend the culprit.
"We are not responsible for the actions of one individual but send our apologies to Dele Alli and everyone at Tottenham Hotspur for this incident.
"We do not tolerate any anti-social, discriminatory or violent behaviour at Arsenal Football Club. Anyone identified will receive a lengthy club ban and their details will be passed to the police to commence legal proceedings."
Alli responded to being struck on the head by the bottle with a '2-0' gesture to the fans and said after the match it made his goal in the victory "a little bit sweeter".
And he posted on social media on Thursday to suggest that the supporter realised they "f*cked up" right before the bottle hit the Spurs star in the head.
It is understood the England international will not face any punishment from the Football Association for his response and the governing body is unlikely to sanction Arsenal either.
Alli set up Son Heung-min for the opening goal on Wednesday before adding Spurs' second with a nonchalant dink beyond Petr Cech.