Officials say the patient was a woman between the ages of 75 and 85 years old. She lived in Pearland.
The county also reported seven new cases on Monday, bringing the county's total to 68.
There are more than 930 COVID-19 cases in the greater Houston area. The death in Brazoria County is the ninth in the Houston area.
Brazoria County issued a Stay Safe at Home order last week. It went into effect on Thursday until 11:59 p.m. on Friday, April 3.
Officials urge residents to follow the guidelines, as the virus is very easily spread. Businesses that remain open are asked to eliminate the congregation of people in groups.
If you have symptoms, have someone in your home that has tested positive, or are elderly or have an underlying condition, you are asked to remain at home at all times.
During the order, residents can still grocery shop and pick up medications from the pharmacy, although they are urged to pick up, deliver, or use curbside. Residents can still walk, bike, or hike in their neighborhood, just not in groups. They can also order takeout from restaurants or use the drive-thru.
It is possible to visit elderly friends and family to run errands and care for them, just be safe and limit interaction.
"Non-essential" businesses were also ordered to close.