The rescuers found "the bodies of a woman and her son, both Belgian nationals, who had been missing after flooding in the Shubak region", about 200 kilometres (125 miles) south of Amman, the General Security Directorate said in a statement.
Her two other children were found alive and well.
"The bodies found after several hours of searching in difficult weather and terrain conditions have been evacuated," the statement said, without giving further details.
The Belgian woman and her three children were part of a group of tourists -- including 14 Czechs -- on an unguided "adventure trip" on Sunday, according to Maan governor Hassan al-Jabur, as reported by the official Al-Mamlaka TV channel.
Authorities evacuated most of the group, but the family went missing, he said, adding rescue teams later found two of the children in "good health".
Jordanian authorities on Sunday evacuated nearly 1,800 tourists from flooding in Petra, a UNESCO-listed World Heritage site.
No casualties were reported after flooding hit the ancient site, according to an official.
Jordan's meteorological authority published a video showing flash floods hitting the Petra, a major tourist attraction.
It showed holidaymakers gathering at the entrance of the Treasury, one of the site's most iconic tombs, before being evacuated.
Similar evacuations have occurred in the past, as the area witnesses increasing rains and storms which scientists say occur more frequently around the world due to climate change.
Petra, famous for its stunning temples hewn from rose-pink cliff faces, was chosen as one of the New Seven Wonders of the World in a 2007 online poll.
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