The closure affects both the upper and lower schools at separate campuses, said Development Director Joyce Limber.
"Since Monday, we've been tracking a significant amount of flu and strep throat," Limber said. "Our concern is for (the students') health and welfare."
Principal Patrick Magee said an average of 200 students stayed home or were sent home for the last three days with the flu or strep throat. Some classes were almost empty, he said.
"Some classes had eight kids in them, and it's a little hard to move forward in instruction when you only have eight kids," Magee said.
The schools have about 840 students.
Magee said closure will give sick students time to recover and allow the administration to sanitize the school.
"We have a whole team and crew coming in over the weekend -- well Thursday through Sunday -- to scrub the school; vents, windows, desks, you name it," he said. "We will be a clean school on Monday with great healthy kids, I hope."
Limber said the decision was made in consultation with the Dallas County Health Department. She said parents were notified Wednesday afternoon by mass phone calls and e-mails.
The decision to close for the rest of the week sits well with parents such as Annette DiCarlo. She has one child at St. Thomas, and another child at a different school. Both are home sick.
"I really am glad for the whole school and for all the kids that haven't gotten sick yet, and I'm glad they won't be sick," she said.
County health experts said they are closely monitoring the situation.
"We're talking about a significant amount of kids," said Zac Thompson, of the Dallas County Health Department. "It was the school's call regarding the closing."
Dr. Doug Hardy, of UT Southwestern, said the flu is hitting Dallas hard.
"This should be a good reminder for parents that the flu is here, it's active, and parents should take their kids to get shots," he said.
Church services will be held this weekend at St. Thomas Aquinas as scheduled.