Vivid Entertainment filed the lawsuit to overturn the law Friday in U.S. District Court in Los Angeles, the Los Angeles Times reported.
The law, called Measure B, requires porn producers to purchase public health permits to film in Los Angeles County. The permits mandate that performers use condoms.
Vivid alleges the law, which was approved by Los Angeles County voters in the Nov. 6 election, is "an unconstitutional prior restraint upon protected expression."
"The exercise of First Amendment freedoms cannot be limited by referendum," the suit said.
"We will fight for our right to express ourselves as we please," Vivid founder and co-Chief Executive Officer Steven Hirsch told the Times.
Hirsch said Vivid suspended filming within the county after Measure B went into effect in December.
Advocates for the condom law say it does not infringe upon First Amendment rights and is a health and safety measure intended to prevent the spread of HIV and other sexually transmitted diseases.
"This is not a free speech issue. This is a workplace safety issue," said Michael Weinstein, president of the AIDS Healthcare Foundation. "If they want to digitally remove a condom" from the final cut of a film, "there's no issue."
County officials have not yet responded to the lawsuit.