The person will be released after the investigation led the police "in a different direction," local authorities say.
"We understand that this may create new concerns in our community," said Mayor Brett Smiley.
The shooting took place at the prestigious university on Saturday local time. All of those killed and injured are students.
Around 11,000 students attend Brown, which is located in the state of Rhode Island and is one of the US's so-called Ivy League universities.
