Hurricane Alex's maximum sustained winds were near 85 mph (140 kph).
A hurricane warning was issued for Portugal's mid-Atlantic Azores Islands, where the Civil Protection Service issued a weather red alert, the highest of four warnings that indicates extreme risk, for five of the archipelago's nine islands.
It said residents should expect waves up to 18 meters (60 feet) high and wind gusts up to 160 kph (100 mph).
The US National Hurricane Center in Miami said in a Facebook post that there hasn't been a hurricane present during the month of January since 1955, when Alice formed in late December 1954 and carried over into the next month.
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Alex was expected to move near or over parts of the Azores tomorrow, the US National Hurricane Center said.
The Azores government today advised kindergartens to stay closed and told residents to ensure drainage systems aren't blocked.
The archipelago, which has a population of around 250,000, has been threatened by hurricanes before but they usually lose their strength as they move into colder northern water.
Alex formed only days after a rare event in the Pacific.
Tropical Storm Pali, only the third such system to develop in January in over 40 years, had weakened to a depression today and was expected to dissipate in the next day or so.
It never made landfall and was no threat to land.