One male was arrested.
The victims — two teachers and one student — were injured by a large, long-bladed knife, say police.
None of the injuries are believed to be life-threatening.
"The intervention by another student to subdue the suspect certainly played a critical role to ensure that a bad situation was not made a lot worse," Fredericton Police Chief Leanne Fitch said in a statement.
"This was an isolated incident, and we do not believe there to be any additional threat to the community," she said.
'Somebody help us'
Police say they received a call about a disturbance at the private career college on Prospect Street at about 8:25 a.m.
Students at the scene said screams from a female and cries for help from a male came from the room where the corrections course is taught.
"We heard girls screaming, we assumed [it] was students," said Shanita Fox-Pelletier, a first-year pharmacy technology student.
"Then we heard a man yell, `Help us please, help us. Somebody help us."
The instructor in the pharmacy technology course initially told students that the yelling was probably an exercise being carried out in the corrections room, but then locked the door.
"It was scary, yeah," said pharmacy technology student Courtney Watson. "It was really scary.
"They were screaming and asking for help and we were like, `That's not a drill.' So we just kind of hid in the classroom."
The college cancelled classes for the day after the incident.
A number of primary response team officers and major crime detectives are working on the file, said Chief Fitch.
"We will work with Eastern College Administration to make sure that those involved in this incident get the support services that they need," she said.