Neither residents nor Cuban state media reported injuries or damage.
Both tremors were centered about 35-40 miles (60-65 kilometers) southeast of Santiago de Cuba, the main city in eastern Cuba.
Yolanda Tabio, a resident of Santiago's historic center, told The Associated Press there was no apparent damage, but that many people left their homes in fear, particularly after the second tremor.
"It was really strong," Tabio said. "First there was a horizontal shake, and then the next one was up and down."
Eastern Cuba lies just across a short stretch of water from Haiti, which suffered a massive earthquake on Jan. 12 that devastated the capital, Port-au-Prince, and left more than 200,000 dead. Eastern Cuba is prone to seismic activity as well.
A magnitude-5.4 quake hit the region on Feb. 12.