The accusation was made during the Lakers' first-round playoff game against the Phoenix Suns but Brown had vigorously denied it, reports The Los Angeles Times.
"Two months ago I assured everyone that I was completely innocent of any wrongdoing," Brown said in a statement. "I am gratified that the authorities have come to the same conclusion and that the matter is being dropped."
The district attorney's office said a medical exam of Brown's accuser revealed no signs of forcible sexual assault.
Brown was quoted as saying, "It is nothing short of despicable that in today's environment completely unfounded allegations can so easily be made against someone in the public eye with no accountability whatsoever."