According to Mundo newspaper, the hurricane hit the country near the city of Figueira da Foz with wind gusts reaching 109 miles per hour.
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Red alert was announced in 13 of 18 districts of the country. The National Authority for Civil Protection recorded about 1,900 incidents overnight, including several road accidents as a result of uprooted trees.
The city of Coimbra in central Portugal was most affected by the disaster, the publication said.
Hurricane Leslie has become the strongest storm in Portugal since 1842.
According to the Spanish State Meteorological Agency, the tropical storm has also reached the continental part of Spain with gusts of wind of up to 60 miles per hour and hit the province of Zamora on Sunday morning. Meteorologists expect the storm to weaken soon.