The extent of their injuries wasn’t immediately clear on Tuesday.
The head of the local police told a news conference that the suspected perpetrator was among the five people shot.
The adult education centre is about 200 kilometres west of Stockholm.
The school, called Campus Risbergska, serves students who are older than 20, according to its website. Primary and upper secondary school courses are offered, as well as Swedish classes for immigrants, vocational training and programs for people with intellectual disabilities.
The violence broke out on Tuesday afternoon (early Wednesday AEDT) after many students had gone home following a national exam. Police vehicles and ambulances, lights flashing, blanketed the parking lots and streets around the school as a helicopter buzzed overhead.
Teacher Lena Warenmark told SVT News that there were unusually few students on the campus because many went home after the exam. She also told the broadcaster that she heard probably 10 gunshots.
Students sheltered in nearby buildings. Other parts of the school were evacuated following the shooting, which began at around 12:30 p.m. local time (1130 GMT).
Andreas Sundling, 28, was among those forced to barricade themselves inside the school.
“We heard three bangs and loud screams,” he told Expressen newspaper while sheltering in a classroom.
“Now we’re sitting here waiting to be evacuated from the school. The information we have received is that we should sit and wait.”
Police said that no officers were shot during the violence.
“The reports of violence in Orebro are very serious. The police are on site and the operation is in full swing,” Justice Minister Gunnar Strömmer told TT.