A statement from UEFA said the Serie A club were under investigation for "racist behaviour of supporters, insufficient organisation and the throwing of missiles and/or fireworks" during the last-16 match.
Tottenham striker Emmanuel Adebayor, who scored his side's away goal in a 4-1 defeat in Thursday's second leg, was allegedly subjected to monkey chants and plastic bananas were waved in one section of the half-empty San Siro.
Tottenham manager Andre Villas-Boas, whose team went through on away goals after the 4-4 aggregate score, told reporters after the game that it was "very easy" to hear the chanting and said he hoped UEFA would act.
Last month, Inter were fined 50,000 euros by the Italian league after fans racially abused their former player Mario Balotelli in a derby with AC Milan.
Meanwhile Lazio, who have a long-standing right wing element among their support, were ordered by UEFA to play two European matches behind closed doors after racism by their fans in Europa League matches against Tottenham, Maribor and Borussia Moenchengladbach.
Italian authorities have long been criticised by anti-racism campaigners for not cracking down hard enough on discrimination in sport.
Italy had appeared to have finally got to grips with its football racism problem in January when Milan's Kevin-Prince Boateng stormed off the field in a friendly against lower league side Pro Patria following abuse from the stands.
The encounter was abandoned, Boateng was praised across the Italian and world game while Pro Patria were ordered to play their next home match in an empty stadium.
The following week, the government's watchdog for sports events said Italian public security officials will be given the power to stop or interrupt matches in the case of racist behaviour by fans.
The ONMS said that, in cases of racism, the referee should alert the fourth official who should in turn report the incident to the public security department responsible for policing at games.