Brad Downey, an American artist based in Berlin, had the charred sculpture of the US first lady removed on 5 July, exactly a year after it was unveiled.
A police spokeswoman told Reuters that the incident, which took place near the town of Sevnica, was being investigated.
The office of Ms Trump in Washington did not immediately respond to a request for comment.
Mr Downey, 39, said he had wanted the artwork to encourage conversation about politics in the US, especially around Donald Trump's anti-immigration policies and his wife's status as an immigrant.
Speaking of those responsible for the fire, he said: "I want to know why they did it."
The sculpture, which was carved from the trunk of a linden tree by a local folk artist before being erected in July 2019, does not bear a close resemblance to Ms Trump.
The unconventional work depicts her in a blue dress, similar to the one she wore to her husband's inauguration in 2017.
Since Ms Trump became first lady, her home town has brought out a range of products named in her honour, including wine and chocolate.
The destruction of the sculpture came as her husband pledged in recent weeks to take firm action against those who damage historical monuments in the US, following the toppling of statues at global anti-racism protests sparked by the death of George Floyd.
Earlier this year, a large wooden statue depicting the US president was burnt in Moravce, a city east of Slovenia's capital Ljubljana.
Additional reporting from Reuters