The 19 students began their protests on 2 February.
They said they will continue until Brown officials consider divesting.
It is likely the longest hunger strike in the US since the beginning of the ongoing Israel-Gaza war.
It is led by both Palestinian and Jewish students, said Ariela Rosenzweig, one of the students striking.
Ms Rosenzweig, 22, said it was inspired by a similar 11-day hunger strike on campus in 1986 which called for divestment from firms operating under apartheid in South Africa.
