Ramsdale was man-of-the-match and made a number of crucial saves to help Arsenal move eight points clear at the top of the Premier League with their first away league win against their local rivals since 2014.
The supporter leapt onto the advertising boards at the side of the pitch to kick out at the England international after Ramsdale celebrated in front of the stand behind his goal and exchanged words with Tottenham forward Richarlison.
"The Spurs fans gave me some throughout the game," Ramsdale told Sky Sports.
"I was giving some back. The people I did give it to greeted it in sportsmanlike terms but one fan tried to give me a little punch on the back.
"It is a shame as it is just a game of football at the end of the day. Both sets of players tried to bring me away but thankfully nothing too drastic happened.
"It is a sour taste but I'm sure we will enjoy it when we go back into the dressing room."
Spurs defender Eric Dier, who had his own confrontation with a fan at the Tottenham Hotspur Stadium in 2020, said the incident was "unacceptable."
The English Football Association said they "strongly condemn" the incident of "wholly unacceptable behaviour", while the Professional Footballers' Association added that these instances were happening too often.
"Players have a right to be safe in their place of work," the PFA said in a statement. "When a player is attacked, we expect the laws 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 that players and staff are better protected in their place of work."
Spurs pledged to take action in a statement released shortly after the match.
"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," Tottenham said.
Spurs coach Antonio Conte said he did not see the Ramsdale incident.
"In every moment you have to show respect," he added. "If we want respect we have to show respect. If it happened then for sure I didn't like it."
Arsenal put on a masterclass to overwhelm shell-shocked Tottenham and extend the gap at the top of the Premier League over champions Manchester City in second, a result Ramsdale played a major role in.
"The manager also mentioned that in the last few North London derbies we haven't kept a clean sheet, so that spurred me on a bit," he added.
