Jeers were ringing out around White Hart Lane as the Cameroon international trudged down the tunnel with his team-mates.
Assou-Ekotto appeared to take exception to comments from one fan and was alleged to have raised his hands to the supporter's throat.
Spurs coach Joe Jordan intervened, bundling the left-back down the tunnel and into the dressing room.
Police were summoned to the scene and the fan was questioned by officers. Assou-Ekotto was also expected to be interviewed.
A Tottenham spokesman said: "We are aware of the incident and we are investigating. We expect all parties to be interviewed by the police.
Spurs manager Harry Redknapp said: "I don't know what it was all about or why someone was having a go at him. They don't see us lose here very often."