The mother was rushed to a nearby hospital where her condition was under control, rescue officials said.
The woman went into labour minutes after being airlifted to safety from Ratnapura district, which is one of the worst flood-hit areas in the country.
At least 177 people have been killed and 104 others missing in the island nation's worst torrential rains in 14 years. The death toll is expected to rise further, according to the Disaster Management Centre.
The flooding is the worst since May 2003 when 250 people were killed and 10,000 homes destroyed after a similarly powerful Southwest monsoon, officials had said.
Sri Lanka, which has been heavily deforested for cash crops, often witnesses landslides during the monsoon season.