Brooklyn resident Dino Tomassetti was taken into custody Saturday in Mahwah, New Jersey, which is about 47 miles northwest of Hewlett Harbor on Long Island, where the shooting happened earlier in the day, police said.
The suspect's 65-year-old father was shot in the back and 64-year-old mother in the head, officials said.
"Both victims were conscious and alert and were transported in a Nassau County Police Ambulance to a local hospital for treatment," according to a police statement.
Tomassetti was being held without bail in Bergen County Jail on a fugitive from justice charge on Monday, pending extradition to New York.
It wasn't immediately clear on Monday if Tomassetti had retained an attorney.
The suspect identifies himself as a personal trainer on social media and has posted numerous pictures from the gym in sleeveless shirts, displaying his muscular arms, shoulders and chest.