The 7.8-magnitude earthquake struck Nepal on April 25 and killed more than 6,000 people.
A huge crowd cheered as rescuers brought the teenage boy out of the rubble in the capital, Kathmandu. The boy has now been taken to a field hospital.
Meanwhile, bad weather is hampering the delivery of relief to remote villages, a Nepal government spokesman said.
The government has been criticized for its response to the disaster.
Outside Kathmandu, the relief effort has relied heavily on helicopters, with mountainous roads blocked by landslides triggered by the earthquake.
In the capital, rescue workers from Nepal and the US worked for hours to free the boy from the rubble of the building.
The 15-year-old boy, named in the media as Pema Lama, eventually emerged blinking into the sunlight, to cheers from a crowd.
He was carried out away on a stretcher with a blue brace strapped around his neck, and has now been taken to an Israeli-run field hospital.
Andrew Olvera, an official from the US Agency for International Development, earlier told the Associated Press news agency that the boy had been trapped between the collapsed floors of the building but was not “too far down”.
Frustration has been growing in parts of rural Nepal over the pace of relief efforts, with some badly-affected villages yet to receive any assistance.
The UN has appealed for $415 million to help provide emergency relief over the next three months. Officials say last week’s quake injured at least 11,000 people.
The UN says more than 8 million people have been affected by the quake and some 70,000 houses have been destroyed.
Despite extensive damage, experts say the number of casualties in many villages was lower than feared because people were working outdoors at the time the quake struck.
In Kathmandu, riot police clashed on April 29 with protesters angry at a lack of transport out of the city and delays in distributing aid. Thousands were waiting for buses to take them to rural areas.
Witnesses said a truck carrying drinking water was forced off the road and protesters climbed on top of it, throwing the bottles into the crowd.
However, there have been some signs that parts of Katmandu are returning to normal.
Some people have decided to return to their homes, having spent several nights in the open. Cash machines have been refilled and some shops and street vendors have once again started trading.
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