It has now passed the US territory and is next set to hit the Dominican Republic. It may also affect the northern coast of Haiti.
In Puerto Rico, Irene cut power to more than a million people, downing trees and flooding streets, the AP news agency reports.
Irene may hit Florida, Georgia and the Carolinas in the US later in the week.
In Puerto Rico, there were no reports of deaths or major injuries, but its governor has declared a state of emergency and asked people to stay indoors.
Irene has maximum sustained winds of 80mph (130km/h), said the National Hurricane Center in Miami. That puts it just above the official strength of a hurricane.
At 13:00 GMT, it was centred about 90 miles (140km) west-north-west of San Juan, Puerto Rico, about 75 miles (125km) east-north-east of Punta Cana in the Dominican Republic, and moving west-north-west at around 14mph (22km/h).
A hurricane warning is in effect for the north coast of the Dominican Republic. A hurricane watch is in effect for the northern coast of Haiti and the central Bahamas.
All of Haiti is under a tropical storm warning.
Haiti, which suffers from extensive deforestation and poor infrastructure, is particularly vulnerable to the heavy rains Irene is expected to bring.
In June, more than 20 Haitians were killed by mudslides and flash floods.
The country is also still struggling to recover from a devastating earthquake in January 2010, which officials said killed as many as 230,000 people, leaving more than 1 million homeless.
According to the International Organization for Migration, some 634,000 Haitians still live in camps; other estimates put that figure at 375,000.
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