Authorities said Varinecz pulled a knife and fought briefly with an officer as school started Friday morning at Carolina Forest High School in Conway.
Horry County schools spokeswoman Teal Britton said the boy asked to speak to the officer. She says the teen stabbed the officer after the two went into an office.
A hospital spokeswoman said the officer was being treated and was in good condition.
The officer has not been identified. A woman who answered the phone at the teen's house said the family had no comment.