The stabbing happened around noon at Castor Gardens Middle School on the 1800 block of Cottman Avenue.
During a news conference on Wednesday, PFT President Arthur Steinberg called it "an epic administrative failure at the school level."
The student managed to bring a knife into school, even though he passed through a metal detector.
RELATED: Student stabs 2 staffers at Castor Gardens Middle School in Northeast Philadelphia
2 staffers stabbed by student at middle school in Northeast Philadelphia: Source
The victims are a 31-year-old woman and a 63-year-old woman. Police say they suffered cuts to the arm and stomach.
The principal described the injuries as "minor."
No students were injured in this incident.
"This is a result of chronic disinvestment that's happened in our schools, so they don't have enough resources, including personnel and equipment," said Steinberg.
The union president says the school did not follow protocol after the stabbing. Instead of a lockdown and an announcement over the public address system, a staffer was the one who warned teachers to lock their doors.
"I want to commend Rashema Haney, the paraprofessional who is one of our members, who ran down the hallway while the assailant was on the loose looking for people to stab, alerting staff members in their rooms not to open the door," said Steinberg.
On Wednesday, he spoke with Superintendent Tony Watlington to demand a full investigation and changes to their security protocol.
He wouldn't go into specifics but says if they aren't remedied, he will spell out the problems to the public.
"They're upset, they are scared, they want to make sure something like this doesn't happen again," said Steinberg.
The 11-year-old has developmental issues, police say, and officers are working with his parents.
The School District of Philadelphia says it is investigating.
"The School District of Philadelphia is focused on the safety and well-being of the entire school community. The student did pass through a minimally-invasive gun detection technology when he entered the building, the device is set up to detect firearms. The Office of School Safety will evaluate safety measures across the District," the district said in a statement.