They said she was 38 and gave only her initials, SG.
The woman was riding in a small truck with a Briton driving, and she was lost as the vehicle tried to cross a flooded road.
The driver was rescued from the water and was not injured. The woman's body was eventually found about four kilometers away.
Last Friday's flooding, caused by torrential rains, forced the evacuation of thousands of people from their homes in central and southern Uruguay.
Many roads were damaged and the government has said it will provide emergency aid to farmers whose crops were flooded.