Sources told ESPN on Wednesday that the Algeria international was spotted masturbating in the courtyard at his residence while looking at a woman living in a flat on the ground floor.
Local police and Ligue 1 club Angers confirmed El Melali's arrest without comment and the player has now issued a public apology for his actions.
"These last few days have been very hard -- mentally and physically," he said on Instagram. "Coping with criticism and judgement is tough. I understand that those who received the information cannot tolerate such behaviour.
"I want to apologise to my family, my friends and the fans of my dear club Angers, as well as my fellow Algerians.
"Everything that happened has affected me, but it has also made me stronger and more aware of the values and principles that I must uphold. Thank you to everybody who has stuck with me during this rough time."
El Melali's offence took place late on Monday and was seen by neighbours, who identified him as the man outside the woman's flat looking through her window and called the police.
ESPN sources said it is the second time the midfielder has been arrested for similar offences and his lawyer Sandra Chirac Kollarik defended her client in Le Courrier de l'Ouest by saying that he was "not targeting anyone, nor was he aggressive."
El Melali, who joined Angers in the summer of 2018 and recently signed a contract extension until 2023, is due to appear in court this summer and risks one year in prison and a €15,000 fine.