The move counters Gov. Kristi Noem, who has repeatedly cast doubt on recommendations from the Centers for Disease Control and Prevention to wear face coverings in public.
The Democrat Evers declared a new public health emergency Thursday, after his initial one expired in May, and ordered the wearing of masks starting on Saturday.
State Public Health Officer Dr. Alexia Harrist said face coverings are essential as people can transmit the virus to others before they feel or show any symptoms.
Americans favor requiring people to wear masks while outside their homes to help slow the spread of the coronavirus, including a solid majority of Republicans.