The ACLU filed the lawsuit in federal court in the Northern District of California on behalf of three student visa holders, including one Yemeni who left the United States and is unable to come back, according to court documents.
The lawsuit is a proposed class-action brought on behalf of nationals who are living or have lived in the United States and are originally from the Muslim-majority nations whose citizens President Donald Trump has temporarily banned from entering the United States, with some exceptions.
The suit is the latest in a series of legal actions challenging the executive order that was issued last Friday. Federal judges in several states have placed limits on the order.
The order set off protests over the weekend at several major airports as immigration and customs officials struggled to interpret the new rules.
The plaintiffs and the members of the class "fear that, in the event they attempt to enter or re-enter the United States, they will be denied permission to do so," the lawsuit said.
It accuses Trump and his administration of violating the free speech, religious freedom and due process rights of those affected by the order, and says it is an attempt to fulfill a campaign promise made by Trump to ban Muslims from entering the United States.
"Senior advisers to defendant Trump have engaged in anti-Muslim rhetoric that provides additional support for the notion that the executive order was prompted by animus toward Islam and Muslims," the suit said.
Department of Justice officials could not be reached for comment late on Thursday.
The ACLU asked the court to rule that the executive order violates the rights of the students and class members and to order the administration not to enforce the travel ban, according to the suit.