Wilders' Freedom Party holds nine seats in the Netherlands' 150 seat parliament.
Call for ban
Wilders also said several chapters in the Quran "call on Muslims to oppress, persecute or kill Christians, Jews, dissidents and non-believers, to beat and rape women and to establish an Islamic state by force".
The publication of the letter comes after a weekend attack on Eshan Jami, a young Dutch politician, who established a group to support people who have renounced Islam.
Jami, who was not visibly injured in the attack, is now under police protection as is Wilders.
"Ban this wretched book like Mein Kampf is banned! Send a signal to Jami's attackers and other Islamic radicals that the Quran cannot be used in the Netherlands as an inspiration or an excuse for violence," Wilders said.
Wilders acknowledged that his plan would not receive majority support in the Dutch parliament.
"I am fed up with Islam in the Netherlands: no more Muslim immigrants allowed. I am fed up with the worship of Allah and Muhammad in the Netherlands: no more mosques," his letter concluded.