Prosecutors said the suspect's death ended the criminal investigation against him, but that they would continue to investigate whether he acted alone.
In a statement, the prosecutors said: "So far there are no indications [anybody else was involved]."
Police who searched the man's house on Thursday found no weapons, explosives or indications of other suspects.
No links with terrorism or ideological groups were immediately uncovered, prosecutors said.
Several members of the royal family had looked on in horror as the car drove through the crowd.
A shaken Queen Beatrix extended her sympathies to the victims in a brief nationally televised address on Thursday evening.
She said: "What started as a nice day ended in tragedy. We are all deeply shocked. We are speechless that such a terrible thing could have happened."
It was not clear how the car managed to enter the parade area, which had been sealed off by police hours earlier.
The attack has prompted officials to review security arrangements for the royal family's public appearances, beginning with Memorial Day next Monday commemorating Dutch victims of World War II, followed on Tuesday by Liberation Day festivities.
NOS, the state broadcaster, said the 71-year-old monarch would attend at least the main memorial ceremony as planned.
Hundreds of thousands of people had flocked to cities across the Netherlands on Wednesday night and Thursday to celebrate the national holiday, which was originally intended to celebrate the birthday of Queen Juliana, Queen Beatrix's mother.