Richard Zavala, the city's parks director, said only the so-called Active Pool would remain closed until an investigation is complete, the Fort Worth Star-Telegram reported.
Myron Dukes, 39, his children Lauren, 8, and Christopher, 13, and a friend, Juanitrice Deadmon, 11, drowned June 16. They were attending a church group meeting in Fort Worth.
One of the children slipped into the pool and the other three victims jumped or fell in as they tried to rescue the child, police said.
The $6 million water gardens was designed by New York architects Philip Johnson and John Burgee. The maze of waterways, fountains and pools was featureed in the 1976 science-fiction movie Logan's Run.