Authorities said Faisal Mohammad, 18, had probably been "self-radicalised," and had not been in direct contact with the militant group.
Police shot and killed Mohammad after he carried out the November attack at the University of California, Merced.
The FBI said agents found IS propaganda on Mohammad's computer.
The US-born student was also found with writings that showed that he had planned the attack in advance. All of his victims survived.
He first stabbed two students in a classroom with a hunting knife, before attacking a construction worker who tried to help them. Mohammed then ran outside and stabbed a university employee.
A month later, a husband and wife killed 14 people at a staff training event in San Bernardino.
The FBI has also described Syed Rizwan Farook and Tashfeen Malik as being "self-radicalised" yet inspired by IS.
A student who stabbed four people at a California university was inspired by the so-called Islamic State group, the FBI has said.