The knife attacks happened at around 11:20am local time. Nobody was killed, but the victims of the violence required medical treatment, the report said.
The attacker was shot dead by a police patrol responding to the emergency reported by witnesses.
Law enforcement is now trying to identify the attacker and establish the motive for his stabbing spree.
Investigators are currently trying to verify a claim that the attacker suffered from a mental illness, the police told TASS.
Footage below allegedly shows the aftermath of a police confrontation with an armed man.
Surgut is the largest city and provincial capital of the Khanty-Mansi Autonomous Area, east of the Ural Mountains. It has a population of over 360,000 and remains a major center for oil and gas production in Russia.
These images were posted on Russian social media, allegedly showing scenes of the violence in Surgut.