The statue on the Paseo de la Gloria walkway overlooking the River Plate was severed at the waist leaving only the lower body and a ball.
City Hall said they do not know who was responsible or the motive for the damage.
"It was the victim of an act of vandalism," the city's culture secretariat said on Tuesday. "The city government is already working on repairs."
The statue was unveiled in June shortly after Argentina lost the final of the Copa America Centenario to Chile on penalties, a defeat that prompted Messi to say he was quitting the national team.
The Barcelona forward, who returned to international duty for World Cup qualifiers in September, is widely loved in his homeland.
He does, however, have his detractors, notably those who are critical of his performances for Argentina, who have lost three major finals in two years, including at the 2014 World Cup.
The walkway has statues of Argentine sports greats including racing driver Juan Manuel Fangio, NBA basketball star Manu Ginobili, golfer Roberto de Vicenzo and tennis players Guillermo Vilas and Gabriela Sabatini.
(Writing by Rex Gowar; Editing by Toby Davis)
