The fan climbed over the advertising hoardings to aim a kick at Ramsdale as the goalkeeper went to collect some personal belongings behind the goal.
The young man raced back into the stands as stewards intervened and Spurs have indicated that behaviour has no place at their home grounds as they begin investigations to punish the culprit.
Tottenham said in a statement: "We are appalled by the behaviour of a supporter that attempted to attack Arsenal goalkeeper Aaron Ramsdale at the end of today's match. Violence in any form has no place in football.
"The club has reviewed its CCTV footage to identify the supporter and will be working with the Met Police, Arsenal and Aaron Ramsdale to take the strongest possible action, including an immediate ban from Tottenham Hotspur Stadium."
Meanwhile, the Professional Footballers Association(PFA), have demanded better protection for players in the aftermath of the incident.
"Violence towards players is completely unacceptable. These types of incidents are occurring too often," a statement read.
"Players have a right to be safe in their place of work. When a player is attacked we expect the laws and regulations that are in place to protect them to be properly enforced.
"As the players' union we treat this as a priority issue. We will be continuing to work with the authorities to demand that players and staff are better protected in their place of work."
Arsenal defeated Spurs 2-0 to extend their lead at the top of the table to eight points.
