He was rushed to hospital for treatment but may have to undergo amputation, according to Tainan mayor William Lai.
Lai said rescuers had been trying to dig him out of the rubble for more than 20 hours but failed as his left leg was trapped.
Doctors were sent in to assess whether removing his leg would help save him, but felt there was not enough room for the operation.
Rescuers eventually dug a hole beneath him and pulled him out.
"I briefly talked to him. He is conscious and could communicate with his sister," he said.
But Lai said he is not sure whether Li will still be able to keep his leg.
Li is the second survivor found by rescuers on Monday morning, the first day of the Year of the Monkey according to the traditional Chinese lunar calendar.
Earlier in the morning, a woman surnamed Tsao was found shielded under the body of her husband and was pulled out alive by rescuers. She was conscious but in critical condition.
Rescuers are still scrambling through the wreckage to search for the rest of Tsao's family.
So far they have been able to confirm signs of life and believe up to four people may be alive.
The 6.7-magnitude quake hit Kaohsiung city at 3:57 am Beijing Time on Saturday, just two days ahead of the traditional lunar New Year. Local monitoring authorities put the scale of the quake at 6.4-magnitude.
At least 38 people have been confirmed dead in the quake, with over 100 people believed to be still buried under the rubble.
Of those killed, including at least 10 children, 36 were found in the Wei Guan building, which was left on its side with twisted metal girders exposed.
Taiwan is frequently rattled by earthquakes. Most cause little or no damage, although a 7.3-magnitude quake, the strongest to hit Taiwan in about 100 years, left more than 2,000 people dead.