Harris County Sheriff's Deputy Thomas Gilliland said authorities received an initial report that the suspect had been wrestled to the ground by a student before campus police arrested him.
At least one injured victim had what appeared to be the blade of a box cutter or an X-Acto knife sticking out of her cheek, student Melody Vinton told CNN affiliate KHOU.
Vinton said she had just left her chemistry class when she saw the attacker stabbing people, aiming at their necks and faces.
Soon, she was trying to help victims, ripping a paper towel dispenser off a bathroom wall to get enough paper to help stem the bleeding.
"I turned around, and there was just blood. Just blood dripping down the stairs, all over the floor, all over everyone's towels on their necks. Just a lot of blood," told KHOU.
The school was on lockdown Tuesday afternoon while authorities combed the campus to ensure no other injured people or attackers were there, Harris County sheriff's spokesman Alan Bernstein said.
While authorities investigated, teachers and students huddled together in locked rooms, said Marianna Sviland, a teacher who was in a faculty workroom at the time of the stabbing.
"Outside the window, I saw cops running around. I saw students running, and I realized something was going on," she said. "It was scary."
Four injured victims "were taken out on helicopters," Bernstein said.
Tuesday's incident comes more than two months after three people were wounded in a shooting at a different Lone Star College campus -- the North Harris campus in Houston.