The US National Hurricane Centre said the eye of the Category 4 storm came ashore over the Yabucoa area.
Maria battered the US Virgin Island of St Croix and killed at least one person in the French territory of Guadeloupe and devastated the tiny island nation of Dominica.
The storm hit just days after the region was punched by Hurricane Irma, which ranked as one of the most powerful Atlantic storms on record and left a trail of destruction on several Caribbean islands and the Florida Keys.
The hurricane centre has hurricane warnings and watches out for the US and British Virgin Islands, Puerto Rico, Culebra, and Vieques, the Turks and Caicos Islands, the southeastern Bahamas and the Dominican Republic from Cabo Engano to Puerto Plata.
Earlier this month, Irma devastated several small islands, including Barbuda and the US and British Virgin Islands, and caused heavy damage in Cuba and Florida, killing at least 84 people in the Caribbean and the US mainland.
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