Schwarzenegger had admitted to fathering a child out of wedlock and keeping it a secret for more than a decade.
Shriver and Schwarzenegger have been separated since May.
Shriver cited irreconcilable differences in the filing.
She requested joint legal and physical custody of their two minor children, Patrick and Christopher. The couple has four children together.
Shriver is asking for Schwarzenegger to pay attorney fees and costs.
Shriver is also asking for spousal support.