The suspects, all academy staff, have been accused of hiring a killer to murder Kermen Basangova, 35.
However, police had been tipped off as to the group's intentions, and the "killer" subsequently agreed to cooperate with the authorities.
Russian media reports said last Wednesday that Basangova, who had initiated a financial audit at the academy, had died in hospital after being attacked near her car. However, it later turned out that the reports on her death were fake, and that police had deliberately leaked them in an attempt to flush out those behind the crime.
The "murder" took place on Tuesday, when the "killer" pretended to stab Basangova. Her friend, also recruited by police, was waiting nearby to take her to hospital, Paradeyev said.
Police attended the "murder" scene and cordoned off the area as if the attack had really taken place and arranged for reports of her death to be leaked by hospital sources.
Basangova's driver was arrested two hours after the "attack" in the act of handing over 500,000 rubles ($14,600) to the "killer." The driver's father, also a staff member at the academy, was arrested later. Basangova's deputy, Vladimir Lukin, 70, was then arrested on suspicion of masterminding the killing.
"We have ample evidence to prove the guilt of those arrested," St. Petersburg's senior investigator, Alexander Klaus, said, adding that the suspects "have admitted to some or part of the crime."
Basangova told reporters on Wednesday the attempted murder was over "major financial violations," including the misappropriation of funds allocated for student halls of residence repairs. Basangova discovered the financial discrepancies after taking over as rector last December.
"The mastermind is unfortunately my first deputy, Vladimir Lukin," Basangova said.
Basangova was elected head of the Polar Academy - which trains members of indigenous ethnic groups in Russia's extreme north, Siberia and Far East as officials to administer the vast regions. She was supported by a teaching staff which included Lukin and his wife, the former academy rector.
