Rescue and search personnel have been immediately ordered to leave the area along the river in heavily affected Kerr County. The risk of a new flash flood is considered high, reports AP.
It is the first time that the search, which has been going on since the disaster on July 4, is interrupted due to the weather. The work is expected to resume on Monday, according to the rescue service.
Large amounts of rain have fallen during Sunday, and the national weather authority (NWS) has warned that the Guadalupe River may rise another 4.6 meters during the afternoon.
"Many smaller roads and bridges are flooded and very dangerous", warns NWS.
On July 4, the river rose eight meters within 45 minutes at dawn, when many were asleep. The floods in Texas claimed at least 129 lives, and 166 are still missing according to NBC News. The city of Kerrville was the most affected.
Local authorities have been criticized for the lack of a warning system in the area, and questions have been raised about whether cuts within NWS have worsened the ability to make quick and reliable forecasts.
The US Secretary for Homeland Security, Kristi Noem, tells NBC News that President Trump is unlikely to abolish the country's disaster agency Fema, but that it will be reorganized.
Previously, Trump has said he wants to "eliminate" the agency.
Noem herself has been accused of delaying Fema's relief efforts in Texas by not giving clearance in time. She rejects the criticism and says she approved the effort as soon as she had the contract in front of her.