The cub, believed to be about five months old, has very little chance of survival unless found in the coming hours, according to authorities in Tarn, a southwestern region in the French Pyrenees.
Weighing a mere eight kilogrammes (18 pounds), it presents "no danger to humans," officials said in a statement.
The little bear, which was separated from its mother before being weaned, was very weak when found in Couflens, a village on the French-Spanish border.
After being caught by agents from France's national hunting and wildlife agency ONCFS, it was taken in by a person licensed to keep wild animals in Saint-Pierre-de-Trivisy, about 100 kilometres (60 miles) east of Toulouse.
No details about how the cub escaped were immediately available.
A team of 12, including three ONCFS wildlife experts, were searching for the animal on Monday.
The authorities appealed for information on any sightings.
About 50 brown bears live on the French side of the Pyrenees mountains that straddle the border with Spain.
France began reintroducing bears from Slovenia about 20 years ago, despite opposition from local farmers, after the native population was hunted to near extinction.