Governor Wanda Vazquez Garced activated security measures on the island and said all public sector offices would remain closed on Tuesday while emergency plans were implemented, Presstv Reported.
The Pacific Tsunami Warning Center (PTWC) reported a small tsunami measuring around 0.02 meters.
The first and biggest quake, of magnitude 6.5, struck at a depth of 10.0 km at 4:24 am (0824 GMT) near Ponce on the island's southern coast, the US Geological Survey said.
A 73-year-old died there after a wall fell on him, newspaper El Nuevo Dia reported.
Puerto Rico has been hit by several quakes in the past two weeks.
The first on Tuesday, which witnesses described on social media as "super strong" and lasting up to 30 seconds, was the strongest yet, and was followed by a number of hefty aftershocks, including one measuring 5.8.
The impact along the country's southern coast appeared significant.
In the town of Guanica, several buildings collapsed. Further east in Maunabo, footage on social media showed residents evacuating to higher ground following the tsunami warning.
On Monday, a 5.8-magnitude quake off southern Puerto Rico knocked several houses off their supporting pillars in Guanica and Guayanilla. Television images showed vehicles crushed beneath them.