Minnie, a Maltese Shih Tzu, escaped after builders left a door open at her family mansion, The Sun On Sunday reports.
The accident happened as the Strictly Come Dancing host was returning home in her Range Rover and the pet ran under her front wheels.
Daly, 49, told the newspaper: “I’m horrified and devastated by this terrible, tragic accident.
“It has had a huge effect on the whole family and we are heartbroken at losing Minnie.
“This has, and continues to be, a very emotional time for us all.”
She described six-year-old Minnie’s death as “a dog owner’s worst nightmare”.
According to the newspaper, Daly was unaware Minnie had got out of the house and did not have time to react when the pet ran under her car.
The accident - which has also devastated Daly’s husband, TV host Vernon Kay, and their daughters, aged 14 and nine - happened last month, days before the family were due to fly to the Maldives.