Flash flood warnings cover the entire island, which continues to be lashed by heavy rain in the storm’s wake.
Maria, now a category three storm, is now lashing the Dominican Republic further west and heading towards the Turks and Caicos Islands.
It is the second devastating storm to hit the Caribbean this hurricane season – the first being category five Irma earlier in September.
Puerto Rico Governor Ricardo Rossello described the hurricane as “the most devastating storm in a century” and said that Maria had hit the island’s electricity grid so badly that it could take months to restore power.
The storm is being blamed for at least 10 deaths across the Caribbean. In Puerto Rico one man died after being struck by a board he had used to cover his windows.
The authorities have warned people to move to higher ground amid “catastrophic” flooding, and with up to 30 inches (76cm) more rain predicted by Saturday.