The suit claims Brengle was diagnosed in November 2016 with a rare condition known as Complex Regional Pain Syndrome Type 1.
"Tennis authorities ignored evidence of her professionally-diagnosed condition and refused to provide alternative testing or a medical accommodation, instead subjecting Brengle to testing that caused her to withdraw from tournaments and has now resulted in permanent swelling and weakness in her serving arm and hand," Ginsberg said in a statement.
The 28-year-old American, ranked 83rd in the world, had never failed or missed a doping test in her 10 years as a professional, the statement said.
The lawsuit said the exact amount Brengle would seek from a jury had yet to be determined but would likely be in excess of $10 million.
The WTA and ITF did not immediately respond to a request for comment.
Brengle said the lawsuit was aimed at forcing tennis authorities to give more thought to the health of players.
"I am bringing this action in an effort to force those who control the sport I love to understand that players are not commodities and should be treated with respect and dignity," she said in the statement.
"The unbridled authority of officials to subject players to the kind of abuse I suffered cannot be tolerated; players must have a say in matters involving our health and safety."
Brengle lost her first round match at the Charleston Open last week.
The lawsuit comes less than two months after Canadian player Eugenie Bouchard reached a settlement in her lawsuit with the U.S. Tennis Association (USTA) after a fall at the 2015 U.S. Open resulted in her withdrawal and a concussion.
