The strongest jolt registered a magnitude of 5.8 at 12:34 p.m. local time about 30 miles southeast of the capital, Guatemala City.
It was preceded and followed by 4.8 magnitude quakes that also caused some damage.
Landslides triggered by the shakings blocked the main Pan American highway in several locations. The roadway connects Guatemala with the rest of Central America.
President Alvaro Colom said there were reports of many injuries across the country, while several buildings and at least a hundred houses were also damaged.
In the capital, the quakes were strong enough to break windows of some high-rise buildings and schools.
The quake swarm struck as Guatemalans were returning to their normal daily routine following a weekend of independence day celebrations.