A spokesperson for the Volunteer Firefighters told media that at least one woman died and three others were injured in a landslide caused by temblors in the southwestern community of Cuilapa.
Among those taken to a clinic were three children from a school who were injured when they ran looking for help.
Media also reported damage to the hospital building and several homes in Cuilapa.
The quakes were felt in the southern, eastern, central and southwestern regions of the country and lasted for more than 20 seconds, according to official reports.
The report from the National Seismology Institute said that the magnitude-4.8 quake occurred at 11:59 a.m. with its epicenter located 61 kilometers (38 miles) southwest of Guatemala City in Santa Rosa province.
The second temblor, a magnitude-5.8, occurred 34 minutes later and its epicenter was located 34 kilometers (21 miles) southeast of the capital.
The spokesman for the Conred emergency management office, David de Leon, confirmed to the media that damages have been reported to houses and buildings in Cuilapa and that rescue teams have been sent to the area.
In Greater Guatemala City, dozens of people ran into the streets in panic seeking protection.