An official with the Murcia regional government said the quakes had magnitudes of 4.4 and 5.2. The epicenter of the quakes was close to the town of Lorca.
Seismologists say the first quake was about six miles deep and centered about 220 miles south of Madrid. The second quake hit in the exact same spot.
The deaths reportedly occurred with the second, stronger quake, which was the largest quake to hit Spain in the last 50 years.
The earthquakes destroyed historic buildings in the southeastern city of Lorca. In a YouTube video, a Spanish journalist was seen reporting from the street in front of a damaged church when a giant section of steeple came crashing to the ground.
Elsewhere, news footage showed how cars parked along the city's cobblestone streets were destroyed by falling debris.
The two quakes hit about two hours apart, and experts said that's what caused the major damage. The buildings were already compromised, and then they were leveled by the second strong quake.
The Spanish Red Cross went into action quickly to help with the dozens who were injured, even as a hospital was evacuated as a precaution.
The Murcia region where the city of Lorca is located is Spain's most seismically active area, but most quakes are too small to be noticed.
According to U.S. seismologists, the quakes hit near a large fault beneath the Mediterranean Sea where the European and African continents brush past each other.
The Associated Press contributed to this report.