Since Vilks was facing death threats for his drawings, it raised the question of whether the crash was a terror attack instead of an accident.
But the Swedish Prosecution Authority said in a statement that it was "a tragic accident" as it announced the closure of the investigation into the October 4 crash after an "extensive analysis, with a technical investigations on the spot and the questioning of witnesses".
"In summary, it is most likely that a tyre on the police vehicle exploded and then the driver lost control of the vehicle, which came over on the other side of the road and collided head-on with the truck," Chief Prosecutor Per Nichols said.
"The extensive investigation now shows that no crime has been committed."
In parallel with the prosecutor's investigation, police had conducted a preliminary investigation into possible murder in the case.
That probe, which also was closed on Wednesday, concluded it was an accident.
Vilks was largely unknown outside Sweden before his Mohammed drawing.
At home, he was best known for building a sculpture of driftwood in a nature reserve in southern Sweden without permission, triggering a lengthy legal battle.
He was fined but the seaside sculpture - a jumble of wood nailed together in chaotic fashion - still draws tens of thousands of visitors a year.
The artist's life changed radically after he drew a sketch of Mohammed with a dog's body.
Dogs are considered unclean by conservative Muslims, and Islamic law generally opposes any depiction of the prophet, even favourable, for fear it could lead to idolatry.
Al-Qaeda put a bounty on Vilks' head.
In 2010, two men tried to burn down his house in southern Sweden and in 2014 a woman from the US pleaded guilty in a plot to try to kill him.
The following year, a free-speech seminar that Vilks attended in Copenhagen, Denmark, was attacked by a lone gunman who killed a Danish film director and wounded three police officers.
Vilks, who was widely believed to have been the intended target of that 2015 attack, was whisked away unharmed by bodyguards.
The gunman later killed a Jewish security guard outside a synagogue and wounded two more officers before he was killed in a firefight with police.
