Though weakened into a tropical storm, it continued to bring heavy rain and blustery winds to the Southeast as it pushed inland, soaking areas still recovering from last month's Hurricane Florence.
Hurricane-force winds have brought down hundreds of trees and left more than 15,000 homes without power in Portugal.
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. Emergency services issued flood warnings for the north and northwest of the country for Sunday afternoon and evening, advising Spaniards to avoid driving in the storm.
The storm formed on September 23 and spent weeks in the Atlantic Ocean before coming to the Iberian peninsula.
But state broadcaster RTP says wind speeds reached 170 kph (105 mph) in the coastal town of Figueira da Foz, 200 kilometers (125 miles) north of Lisbon.
Luis Belo Costa of Portugal's National Protection Agency, who gave the injury toll, said none of the injuries were life-threatening.
Meteorological records indicate that only five hurricanes have ever arrived in this part of the Atlantic Ocean, and Leslie could turn out to be the most powerful storm to hit Portugal since 1842. Even Portugal's main highway was temporarily blocked by fallen trees.
Four departments in southern France have also been put on alert for storms and flooding.
Leslie moved east on Sunday across the Iberian Peninsula to Spain, where authorities issued warnings for heavy rains and storm conditions for the northern part of the country.