Eight people were injured and taken to hospital and many areas suffered from flooding. Television footage showed a funnel-shaped rotating column of air approaching the shore from the Atlantic near the town of Lagos.
Meteorologist Maria Frade said the weather phenomenon "definitely resembled a tornado judging from the video", but would not immediately confirm if it was one.
Firefighters said most of those injured had to be pulled out of overturned vehicles.
Algarve is a popular tourism destination, although November is low season.
Tornadoes are not common in Europe, but do occur occasionally in the northwest and south of the continent. (Reporting By Andrei Khalip; Editing by Pravin Char)
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