Diego Pillco, 19, was charged with second degree murder after several hours of questioning by police, WABC-TV, New York, reported.
The cause of Shelly's death has not been released. She was found hanged in the bathroom of her family's home by her husband, Andy Ostroy, Wednesday.
Despite all evidence to the contrary, Ostroy refused to believe his 40-year-old wife killed herself, WABC said. He said it did not make sense in light of her success as an actress, screenwriter and director as well as her devotion to their 2-year-old daughter. There was no suicide note at the scene.
Police Monday said Pillco and Shelly argued before her death, but did not release any more details.
Ostroy released a statement Monday night thanking New York City police for "their dedication, professionalism and tenacity in following up on every lead in this case."
He went on to request that "everyone will respect that this is a difficult and private time for our family."
Shelly was best known for roles in the indie films "Trust" and "The Unbelievable Truth." She starred in "Factotum" with Matt Dillon last year and at the time of her death was getting ready for the release of "Waitress," which she wrote and directed.
Notable deaths of 2014 [PHOTOS]