Goodger, who stars on the program "The Only Way is Essex," said she was "mortified and humiliated."
The clip, reportedly filmed without her knowledge, allegedly shows her and ex-boyfriend Jake Mclean, a property developer, in a bedroom they shared.
"Anyone caught sending private, intimate stuff like this should be arrested," Goodger said.
"I didn't make a sex video like Kim Kardashian or Paris Hilton. I'm a grown woman and I've not done anything illegal."
Goodger does not think she was the intentional victim of revenge porn, but believes more must be done to prevent such footage from circulating.
"I've got no control over the situation I am in," she said. "I feel powerless. My private life has been invaded in the most horrible way."