Ramsdale was kicked in the back by a supporter as tensions spilled over after Arsenal won 2-0 at the Tottenham Hotspur Stadium on Sunday.
The FA and the Met Police are looking into the incident and Spurs say the fan faces an “immediate ban”.
A Tottenham statement said: “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.”
Ramsdale went to gather his water bottle when a supporter from behind the goal rushed forward and kicked him before climbing back over a number of rows of seats.
The PFA have condemned the incident.
"These incidents are happening far too often. Players have a right to be safe in their place of work," said the PFA.
"When a player is attacked, we expect the laws and regulations that are in place to protect players to be properly enforced.
"As the players’ union, we treat this as a priority issue. We will continue working with the authorities to demand players and staff are better protected in their place of work."
A statement from the FA said: "We strongly condemn the incident involving a spectator that followed today’s Premier League fixture between Tottenham Hotspur and Arsenal.
"This is wholly unacceptable behaviour and we will work together with the police, the relevant authorities and the clubs to ensure the appropriate action is taken."