The Gunners won a memorable match 4-2 on Sunday and London's Metropolitan Police afterward confirmed there were seven arrests made, AFP reported.
Britiain's Press Association said it understands that one of those arrests came after a banana skin was hurled from the away end as Aubameyang celebrated scoring in front of the Tottenham fans.
"Behavior such as this is completely unacceptable and the supporter in question will be issued with a ban," a Tottenham spokesman said.
There were also six arrests for public order offences – at least two of which are believed to be Arsenal supporters who lit smoke canisters during the match.
Former Arsenal and England forward Ian Wright, speaking as a pundit on BBC television, said, "I've played against Spurs and I've taken a lot of abuse from Spurs but never ever has it been racial.
"Now Spurs have to deal with this because some idiot has done that.
"It's not only embarrassed Spurs but it has embarrassed the Premier League because it has gone around the world, and now Spurs have to deal with that and have that tainting all over them. It's really unfortunate to see."
Gabon forward Aubameyang opened the scoring on Sunday with his 10th-minute spot-kick and, after Tottenham had replied through Eric Dier and a Harry Kane penalty, then equalized early in the second half.
Alexandre Lacazette put the host 3-2 up before Lucas Torreira added Arsenal's fourth.
Aubameyang had opened the scoring before an Eric Dier header and a Harry Kane spot-kick sent Spurs in ahead at half-time.
The Gabon forward went on to equalize, with Arsenal wrapping up the points through Alexandre Lacazette and Lucas Torreira strikes.
The unrest was not restricted to the stands as the two sets of players had to be separated following Dier's equalizer on a feisty afternoon in north London.
The England midfielder celebrated by putting his finger to his lips, with Arsenal substitute Stephan Lichtsteiner reacting angrily to the gesture and referee Mike Dean showing Dier a yellow card.