Students at the Lutheran Church-owned Sebastian Kolowa Memorial University in Lushoto, near the border with Kenya, climbed out of windows and ran into the forest to escape.
A mob attacked the university, which is attended by mainly Christians, and set fire to parts of the campus.
The Christian group, World Watch Monitor, which works in the region, said that a lot of the students have been left with injuries and are still recovering from smoke inhalation.
Local media have been told the attackers were heard talking about the best way to kill the students.
The unnamed witness said men broke down the door, covered the floor in petrol and told her not to move.
The attackers left once a fire had begun.
In April 2015, almost 150 Christian students were killed at Garissa University in an Al-Shabaab attack in neighbouring Kenya.
World Watch Monitor says the attack took place earlier in the week and it was a security guard who was killed.
