A former McDonald’s employee who says a manager at a Michigan store grabbed her breasts and buttocks is suing the chain, blaming her mistreatment on what she calls a culture of sexual harassment at the fast-food company.

The former employee and the American Civil Liberties Union filed the suit in state court on Tuesday, as hundreds of McDonald’s employees in Michigan prepared to go on strike to protest the company’s handling of such allegations and demand a labor union. It increased the scrutiny of McDonald’s a little over a week after its chief executive, Steve Easterbrook, was fired for having a relationship with a subordinate.

In the complaint, the employee, Jenna Ries, said a manager at a McDonald’s in Mason, Mich., repeatedly harassed her between 2017 and 2019. She said the manager had groped her, called her offensive names and put his penis in her hand while he was working next to her in the kitchen. The manager threatened to fire Ms. Ries for rejecting his sexual advances, the complaint said, and harassed “many other women and girls.”

The store is owned by a McDonald’s franchisee, but the suit, the latest of dozens of sexual harassment complaints filed by McDonald’s employees in recent years, argued that the problem lies with the chain itself.