The sculpture was discovered only in Buenos Aires in June, but is now in need of urgent repair after they removed the head, arms and torso.
The statue is one of several awards for Argentine sports stars with Glory Street in the capital of that country.
It was built last summer after Messi announced his decision to retire from international football. Later, he decided to remain available to the selectors.
Even as the police did not make any announcements about the perpetrators.
"The statue of Lionel Messi ... was the victim of an act of vandalism that left the sculpture is a soccer player without its top half," said the municipal government of Buenos Aires in a statement.
"The city government is already working on a fix."
Vandalism occurred hours before Messi missed the FIFA Player of the Year Award for longtime rival, Cristiano Ronaldo.
Wizard Barcelona did not attend 'The Best' ceremony in Zurich, partly to avoid playing second fiddle to Real Madrid.
Sign up here with your email
ConversionConversion EmoticonEmoticon