Jonnson filed the $2.5 million lawsuit against CrossFit Thursday in Santa Cruz, Calif., accusing the fitness company of discrimination, intentional infliction of emotional distress and unfair competition.
Jonnson said she should be eligible for the women's division of the competition because she had a sex reassignment surgery in 2006 and is legally recognized as a woman in the state of California.
CrossFit said that since Jonnson was born a male, she must compete in the men's division.
"The fundamental, ineluctable fact is that a male competitor who has a sex reassignment procedure still has a genetic makeup that confers a physical and physiological advantage over women," the company said. "Our decision has nothing to do with 'ignorance' or being bigots -- it has to do with a very real understanding of the human genome, of fundamental biology, that you are either intentionally ignoring or missed in high school."