Lisbon was the worst affected and Figueira da Foz, Averio, Viseu and Porto also suffered damage. The main A1 motorway was among the roads temporarily blocked.
Luis Belo Costa of Portugal's National Protection Agency, who gave the injury toll, said none of the injuries were life-threatening.
The storm, carrying winds of up 100 km/h, was most intense during the night.
A resident of the town told SIC television: "I have never seen anything like it, The town seemed to be in a state of war, with cars smashed by fallen trees". "People were very anxious".
Leslie was set to make landfall in the Lisbon area overnight on Saturday, by which time it is expected to have been downgraded to a tropical storm.
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But Leslie was still expected to generate ocean swells that would affect Madeira, the Azores and the Canary Islands throughout the weekend, in addition to the Atlantic coasts of Spain, Portugal and Morocco. By Sunday morning the powerful winds and heavy rains had mostly subsided.
Flood warnings have also been issued in the north and northwest of the country for today.
Michael, the third most powerful hurricane ever to hit the US mainland, smashed into Florida's northwest coast near the small town of Mexico Beach on Wednesday as a Category 4 hurricane with 155-mile-per-hour (250-kilometer-per-hour) winds.
Leslie first became a sub-tropical storm almost three weeks ago on September 23.
Only Hurricane Vince has made landfall on the Iberian peninsula over the last 176 years, hitting southern Spain in 2005, according to weather records.