The five victims in question all suffered gunshot wounds or broken bones during Tuesday's attack, in which a graduate of the school No. 175 is alleged to have attacked with a gun, leaving nine dead and 23 wounded, reports dpa news agency.
Most of the victims were students.
Nine of those injured were transferred to medical facilities in Moscow on Wednesday.
All managed the trip with no problems, said the spokesperson.
"The doctors are doing everything in their power to save their lives and restore their health," she said, adding that the condition of one child was particularly critical.
The 19-year-old suspect was remanded into detention for two months late on Wednesday.
Authorities will work up a psychological profile to try to determine his level of culpability.
He faces murder charges.
Moscow, May 13
Five children injured in this week's school shooting in the Russian city Kazan remain under close observation but are "stable", a spokesperson for the Tatarstan regional government said on Thursday.
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