South Dakota Governor Kristi Noem wrote to several tribal leaders last week saying the checkpoints were illegal.
But the Sioux say they are the only way of making sure the virus does not enter their reservations.
Their limited healthcare facilities would not be able to cope with an outbreak, they say.
At present, people are only allowed to enter the reservations for essential business if they have not travelled from a Covid-19 hotspot.
They must also complete a health questionnaire before doing so.
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