Milan police attended a hotel in the centre of the city in the early hours of Thursday morning and found more than 20 people in a restaurant, the report from the news agency ANSA said, as Lukaku hosted a party to celebrate his 28th birthday, which fell on Thursday.
Regulations in Milan, which is in one of Italy's Yellow Zones, include a curfew between 2200 and 0500 with breaches resulting in fines.
Lukaku had scored a last-minute goal in Inter's 3-1 home win over AS Roma a few hours before the party.
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Neither the club nor Milan police responded immediately when approached for comment by Reuters.
Italy reported 251 coronavirus-related deaths on Tuesday against 198 the day before, the health ministry said, while the daily tally of new infections rose to 6,946 from 5,080.
In total, Italy has registered 123,282 deaths linked to Covid-19 since its outbreak last year, the second-highest toll in Europe after Britain and the seventh-highest in the world. The country has reported 4.1 million cases to date.
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