A complaint had been made to the police but was withdrawn on Monday.
The full-back is set to meet the supporter he clashed with after Saturday's defeat to Wolves to bring an "amicable" end to the matter.
Assou-Ekotto confronted the supporter next to the tunnel at White Hart Lane moments after the final whistle of the 1-0 defeat and had to be pulled away by Spurs assistant boss Joe Jordan, who then led the 25-year-old Cameroon international down the tunnel.
Emotions running high: Benoit Assou-Ekotto clashed with a Spurs fan following the 1-0 defeat against Wolves on Saturday
Police said on Sunday they were investigating "an allegation of assault"' in relation to the incident, while the Football Association were awaiting reports from the game before deciding whether to investigate.
However, a statement from Tottenham read: 'The club takes the conduct of our supporters and players, and the relationship between them, very seriously.
'We understand that the supporter has now withdrawn the complaint and that he and Benoit are due to speak this week to bring an amicable end to the matter.'
Harry Redknapp's men were jeered off after the defeat to Wolves which dented their hopes of maintaining a challenge for the Champions League this season.
They had already lost to Stoke at home this season and Redknapp said: 'We haveto pick ourselves up on Wednesday against Manchester City.
'You have days it goes your way, some days it doesn't.'
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