Irene brought high winds and torrential rain to Puerto Rico, cutting electricity to about 800,000 people.
Forecasters at the National Hurricane Centre in Miami say Irene will strengthen further as it heads north-west towards the Bahamas.
Irene is generating winds of more than 150km/h (95mph), and 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 as Irene ripped across the island, uprooting trees.
The storm cut power to more than half the island, while water supplies to more than 100,000 people were affected.
The governor of Puerto Rico, Luis Fortuno, said the worst-hit area was the east coast, from Fajardo to Yabucoa.
He said he had asked the US government to declare Puerto Rico a disaster area so it could gain access to emergency funds.
A hurricane warning is in force for the north coast of the Dominican Republic, eastward from the Haitian border.