Demand has soared because of extremely cold weather across the state since Tuesday. New Mexico Gas Company said rolling blackouts in West Texas also impeded the delivery of natural gas to New Mexico.
Martinez declared a state of emergency for the entire state, urging residents to turn down their thermostats, bundle up and shut off appliances they don't need for the next 24 hours.
She later announced all state operations not providing critical services would be closed Friday to decrease the strain on energy resources throughout New Mexico.
"Due to statewide natural gas shortages, I have ordered all government agencies that do not provide essential services to shut down and all nonessential employees to stay home" on Friday, Martinez said after meeting with public safety personnel in Albuquerque.
"I have also encouraged all schools that have not already announced closures to strongly consider doing so," she said.
New Mexico Gas Company said service was disrupted throughout the state - in Bernalillo, Placitas, Taos, Questa, Red River and parts of Albuquerque, Silver City, Alamogordo, Tularosa and La Luz.
Emergency shelters were set up in several areas. Martinez said residents needing help finding a shelter or getting to one should call the non-emergency police or fire phone number in their community.
"As New Mexicans, we've always gotten through difficult situations," Martinez said. "We will get through this situation as well."
Earlier Thursday, Taos Mayor Darren Cordova declared a state of emergency in the northern New Mexico community after gas service was disrupted. He urged area residents to conserve electricity to prevent an outage of that energy source.
Martinez also urged people to curb electrical use to prevent blackouts and allow compressors to function so the state can get natural gas supplies.
"The use of electricity and the use of natural gas are not isolated; one is impacting the other," she said.
The state's largest electrical utility, Public Service Company of New Mexico, asked customers in the southern New Mexico communities of Alamogordo, Tularosa and Ruidoso to reduce their use of electricity because a transmission line serving the area was over capacity.
The overload occurred because a second line into the area was out of service, but PNM said crews were repairing that line.