Ibrahimovic, who sources have told ESPN FC could yet play for Hammarby, and who began his career at Malmo and is Sweden's record international goalscorer with 62 in 116 games, was honoured with a statue in October.
Video on social media showed the statue being torched on Wednesday evening in Sweden, while a racist message was reportedly spray-painted next to it.
"Several people are said to have vandalised the statue and sprayed it with paint," police spokesman Jimmy Morin told state broadcaster SVC, adding that an investigation into the vandalism had been opened.
A fence has since been placed around a statue and security guards have been dispatched to keep watch.
Earlier on Wednesday the monument was also vandalised with a toilet seat and a sheet to cover the former Sweden international's head, while supporters of Malmo began an online petition to have the statue removed.
Malmo fans are angry not just that Ibrahimovic wants to make another club better than his boyhood team but also that he said he didn't think Malmo supporters would be disappointed by his choice.
"A betrayal became a betrayal and a provocation," Kaveh Hosseinpour, vice chairman of Malmo's official supporters group, told The Associated Press. "So he basically stuck a knife in our backs, and then he came along with a sword and chopped off our heads."
Hosseinpour blasted Ibrahimovic for thinking he was "above criticism, that he is above Malmo FF and our feelings just because he is Zlatan.
"The statue is completely worthless now, just a piece of junk," Hosseinpour said. "The best way to solve that was if it was removed and put somewhere in Stockholm or something.
"Every game we go to, we are going to pass Zlatan knowing that there is a statue of an investor in Hammarby, not the statue of the football player Zlatan Ibrahimovic anymore."
The former Manchester United, Juventus, Barcelona and Paris Saint-Germain player is a free agent after leaving the Galaxy this month.
During his time in MLS, he scored 52 goals and assisted 17 more in 53 starts for the Galaxy and arguably became the marquee player of the league, winning MLS Newcomer of the Year in 2018 and twice being selected for the MLS Best XI.
Ibrahimovic earned $7.2 million this past season, according to the MLS players salary database. He made $1.5 million in 2018.
Information from The Associated Press and Reuters was used in this report.