In a post on Twitter, the football unit of the Metropolitan Police, whose officers were on duty for the first leg at Wembley, wrote: "Police have arrested a 17-year-old male for a racially aggravated public order offence at tonight's @SpursOfficial v @ChelseaFC.
"The male is currently being dealt with at a North London police station."
An earlier post from the force had read: "We are working with London football clubs to ensure hate crime, including racism and anti-Semitic language, is tackled robustly.
"Any instances of such behaviour will be taken seriously and thoroughly investigated."
The incident is the latest instance of alleged racist behaviour to shake the top tiers of European football in recent weeks.
Manchester City's Raheem Sterling was subjected to abuse from the stands during his side's defeat at the hands of Chelsea at the beginning of December, with the man responsible later identified and banned from Stamford Bridge.
Police have arrested a 17 year old male for a racially aggravated public order offence at tonight's @SpursOfficial v @ChelseaFC The male is currently being dealt with at a North London police station.— MPS Football Unit (@MPSFootballUnit) January 8, 2019
The club was subsequently punished with two games to be played behind closed doors, a sanction that they declined to appeal.