Humphreys County Emergency Management Agency said rescuers were going house to house and digging through rubble for about 40 people unaccounted for in the area, directly west of Nashville.
Video from the area showed homes caved in and cars wrecked by the floodwaters. Authorities said five or six teams of rescuers were searching through the destruction, some using dogs trained to find people.
Tennessee Governor Bill Lee, a Republican, said late Sunday he would request emergency assistance from the federal government in the next few days after an initial assessment.
President Joe Biden said federal emergency officials will coordinate with the state to offer assistance. Record rainfall of up to 17 inches drenched some areas, sparking massive flooding on Saturday afternoon and evening. Especially hard hit was the Humphreys County town of Waverly, about 55 miles west of Nashville. Hundreds of homes were left uninhabitable.
Waverly Mayor Wallace Frazier told the Tennessean newspaper that those killed in the flooding ranged in age from babies to the elderly.
The Washington Post, citing family members, reported that 7-month-old twins died after they were swept away from their parents' arms.