"Of course she would be removed. I will personally give instructions to the centre myself so that they will implement the correct measures that are needed," Mutko told the agency R-Sport.
The 2008 Olympic gold medallist Kaniskina, 30, who had finished competing, was banned for three years and two months backdated to 2012.
Olympic walk champions Valery Borchin and Sergei Kirdyapkin were also among five athletes banned for doping, the Russian Anti-Doping Agency (RUSADA) said on Tuesday.
RUSADA said the breaking of anti-doping rules "was due to abnormal blood levels in their biological passports".
Kaniskina would not be drawn on her future.
"I won't make any comments until there are instructions from the directors. I am the director!" the newspaper Sovetsky Sport reported her as saying.
The publication also reported the president of the Russian Athletics Federation (VFLA), Valentin Balakhnichev, is ready to step down.
"If I am asked, I will do this. My own personal ambitions are not higher than those of Russia," he said.
"Therefore if they tell me: It is your fault, get your things and go, I will get my things and go without a question," Balakhnichev added.
(editing by Justin Palmer)
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