Supporters gathered outside the stadium after Manchester City's 2-1 defeat against Chelsea at Stamford Bridge on Thursday confirmed Jurgen Klopp's side as league champions, with seven games to spare.
Huge crowds of fans sang songs and let off flares outside Anfield, prompting warnings from police concerned about mass gatherings ignoring social distancing measures.
Merseyside Police closed roads around Anfield at 11pm and advised motorists to avoid the area.
"I would like to congratulate Liverpool FC on deservedly winning the Premier League title, and thank the thousands of Liverpool fans across Merseyside who celebrated at home, as they have for the previous games played behind closed doors," the assistant chief constable said.
"The overwhelming majority of fans have recognised the fact that now is not the time to gather together to celebrate, and chose to mark the event safely. They are a credit to this city.
"Unfortunately, as we have seen throughout the lockdown period, not everyone adhered to the regulations in place. Although the vast majority of celebrations were good natured, a large number of people chose to gather outside the stadium.
"In the days ahead, we urge supporters to do the right thing and celebrate safely with members of your household and in your social bubble. By doing this you keep yourself, your family, friends and neighbours safe.
"As we all know, Merseyside has been disproportionately affected by the COVID-19 pandemic and we must all do what we can to prevent further cases and deaths in our communities.