Vilks, 75, who had been living under police protection since the drawings were published, was traveling in a police vehicle which collided with a truck. Two police officers were also killed.
“This is a very tragic incident. It is now important to all of us that we do everything we can to investigate what happened and what caused the collision,” Swedish police said in a statement on Monday.
“Initially, there is nothing that points to anyone else being involved.”
Most Muslims consider any depiction of the founder of Islam as offensive.
Since the publication of the cartoons, Vilks had been living under round-the-clock police guard following threats against his life. He had a bounty put on his head and his house was fire-bombed.
In 2015, one person was killed in Copenhagen at a meeting meant to mark the 25th anniversary of an Iranian fatwa against British writer Salman Rushdie, which Vilks attended.
Vilks was widely seen as the intended target.
Vilks had said that the cartoons were not intended to provoke Muslims, but to challenge political correctness in the art world.
Swedish ‘Mohammed’ cartoonist Lars Vilks killed in car crash