The arrest took place on Sunday morning, local time, and police are not currently looking for any other people, NBC writes.
All those killed and injured were students, Brown's principal Christina H Paxson said.
Our focus now is to support those affected, the families of the two students who lost their lives today, says Paxson.
At 11 p.m. local time, police released a clip from a surveillance camera showing the suspected shooter near the university.
It had been about seven hours since the school's alarm system sent out warnings of an ongoing shooting.
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.
US President Donald Trump has been briefed on the situation.
