The order requires businesses with four or more rapid responses of COVID-19 cases reported within in a 14-day period to close for two weeks.
More than 25 essential businesses were shut down as of Monday afternoon, including a number of grocery stores and major retailers.
The closures include two Walmarts in Albuquerque and one in Santa Fe, an Albertson's in Roswell, a Smiths Food & Drug Center in Albuquerque and New Mexico Food Distribution Center in Albuquerque.
The state's environment department has published a complete list of businesses that have been closed due to employees testing positive for COVID-19, as well as a watch list, and FAQ about the watch list.
Access to purchase food is now limited because of another order issued by the governor requiring capacity limitations at all stores. New Mexicans are now waiting outside, standing in line for up to two hours, local news reports indicate, which the governor's office has disputed.