Arsenal say they have identified an image of the fan who threw a bottle at Dele Alli during Wednesday's Carabao Cup game against Tottenham, and are working with Metropolitan Police to apprehend the suspect.
The club also apologised to Alli and said "we have all been embarrassed by the individual" who threw the bottle, which hit the Spurs midfielder in the head shortly after he had scored the second goal in Spurs' 2-0 victory.
"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," Arsenal said in a statement. "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."
Earlier on Thursday, Metropolitan Police also issued a statement confirming that they are investigating the incident.
"The Met is working with Arsenal Football Club to identify the person responsible for an incident where a bottle was thrown onto the pitch during the Arsenal vs. Tottenham match on Wednesday, Dec. 19," the statement said. "There has been no arrest in relation to this specific incident."
However, Metropolitan Police said that seven arrests were made in connection to the game "for a variety of offences including possession of drugs; public order and assault on police."
The club said that it was also investigating an incident of alleged antisemitism after British media reports said that one individual was removed from the stands for discriminatory chants.
Alli shrugged off the incident after the game, telling Sky Sports that it "made the goal a little bit sweeter."
After the match, Spurs manager Mauricio Pochettino labeled the bottle thrower "stupid," and that Arsenal should be grateful for Alli's "honest and professional" reaction to being hit.
"It was an amazing reaction," Pochettino told a news conference on Thursday. "Dele was so honest and professional and he behaved really well. His behaviour was top.
"I think the Arsenal people, the club, must be grateful with him because maybe in different situations the player can go down and create a massive problem, and that should be very difficult to manage for the referee, for the people there.
"Sometimes people criticised him in the past in some actions during games, but it's good now to praise him.
"Of course he's more mature now but still he's a kid, he's so young. But he's so clever and he's more mature now, and it's normal, all the process. We're all growing and learning.
"But I think it's a situation that, when I think of that, I hate this type of situation, this action. I know very well that Arsenal are going to take the responsibility and fix the problem but of course we need to praise Dele because his behaviour was fantastic."
Asked if Arsenal should receive a stadium ban, Pochettino said: "It's not fair for Arsenal, the club, the fans -- to pay for one [person].
"I don't know how to call him because it's so strong the word I [could] use. What word can I use? I don't want to be wrong but I think everyone realises.
"People have to behave and celebrate and support your team, but in the right way. It's such a dangerous thing. If rather than the bottle hitting him on his head it had been his eyes, we're then talking about a very bad, serious thing."
Information from ESPN FC's Ben Pearce was used in this article.