Nazarbaeva, who is an influential lawmaker, also says Kazakhstan must improve its labor legislation and see that foreign investors abide by it.
"The time has come for us to stop behaving like an obedient colony that bows to a foreign gentleman whose name appears on the 'Forbes' magazine list [of world's billionaires]," she wrote.
There is no immediate reaction from Arcelor Mittal.
A gas blast in September killed 41 Kazakh miners and triggered protest rallies. The group has since agreed to raise the monthly salaries of its employees to the equivalent of at least $700.