The seafood businessman filed the papers Jan. 3, requesting La Rue not receive spousal support, People magazine reported Friday.
The couple were married for three years and Cappuccio was La Rue's third husband.
La Rue posted on Twitter Thursday, saying she and her 12-year-old daughter Kaya were going through an "emotional time."
La Rue, 47, told People in 2008 she had no plans to marry for a third time after two failed marriages.
"I told [Cappuccio], 'I'm looking for a long-term companion, but I don't see the sense in getting married again,'" she said.
"But within a month or two, we were both on the wedding train."