Organizers referred to the practice as inhumane and believe the Karnes County Residential Center should be closed immediately.
Members of the group also alleged mistreatment of the people being held at the center.
"One of the biggest problems with this facility is that it's run by a private company, and the problem with that is that they aren't answerable to us, the people. They answer to their shareholders," said Cristina Parker, immigration projects coordinator at Grassroots Leadership. "So they have not given us any kind of response or anything, which is exactly why it needs to stop."