The stabbings happened before noon, the Harris County Sheriff's Office said.
Harris County Sheriff's Office spokesman Alan Bernstein said authorities haven't determined if more than one suspect was involved in the attack.
Capt. Robert Rasa of the Cy-Fair Volunteer Fire Department said four people were flown by helicopter to Memorial Hermann-The Texas Medical Center in critical condition, and that two others were taken there with injuries not believed to be life-threatening.
The other victims had minor injuries and were taken to North Cypress Hospital, Rasa said.
Officials said investigators are trying to determine what sparked the stabbings.
College officials issued an alert warning people to seek shelter if they're on campus and telling those not on campus to stay away from the area.
People at the scene have said via Twitter that the campus has been locked down.
This is Lone Star College's second violent incident in recent months. In January, three people were wounded in a shooting at another campus in North Harris County.