The school has a boarding house, meaning students were on the grounds when the attack occurred.
Classes will run as usual today, with the school saying students are not in danger.
But some parents say they'll stay with their children until police catch the offender.
"I won't be dropping her off until I have a little bit more information. I'd just like to know if they've found the person who attacked the security guard," the mother of one pupil told the Nine Network.
It's been reported the guard was stabbed at the school's performing arts centre.
The guard has been taken to Brisbane's Princess Alexandra hospital in a stable condition and will undergo surgery.
"It looks like he's disturbed an intruder. He was stabbed multiple times," a police spokeswoman said. "The offender fled. Multiple police units are hunting for him."
Somerville House spokeswoman Sarah Dreaver says the school will be open and counselling will be offered to any students who need it.
"The students are not in any danger," she told ABC radio. "Our thoughts and prayers are with the security guard and his family at this time."
Somerville House was established in 1899 and is a day and boarding school for girls from Prep to Year 12. It's also a co-educational school for pre-prep girls and boys. AAP has sought comment from the hospital.
- AAP