Leguizamon said he was red-carded because Reyes was in a bad mood because she had not had sexual intercourse.
"San Martin expresses solidarity [with Reyes] not just because she is a woman but also because she is the authority in control of the match and therefore deserves obedience and respect," the club said in a statement.
The team's general manager, Alvaro Barco, said: "Leguizamon is leaving because he damaged our image in the eyes of the public."
Leguizamon also criticized Peruvian soccer, saying, "It's reality. How long has it been since Peru went to the World Cup? How long is it since Peru won anything?"
Peru last qualified for the World Cup in 1982.