The infant, a baby girl named Refi, was found under a pile of broken concrete and rubble.
She was later taken to hospital and given emergency aid by paramedics.
At least 142 were killed in the disaster, but the National Disaster Mitigation Agency (BNPB) stated they anticipated the death toll to rise after all the rubble is cleared away from over 13,000 buildings which have been destroyed.
Sutopo Purwo Nugroho, BNPB’s spokesman, also confirmed that over 84,000 people have been displaced following the earthquake.
Around 4,600 international and Indonesian tourists have been evacuated from smaller islands as the rescue operation continues.
Luke Turner, a British tourist who was on the island on Lombok at the time of the earthquake, said there are “hundreds” of Britons still trying to get off the island.
Mr Turner managed to travel back to the Indonesian capital of Jakarta, but described the chaos inflicted on the local population.
Speaking to the BBC, he said: “The flight was just awful.
“There were locals that were on there to flee the island that were in floods of tears.
“It was just the most eerie flight.
“We haven’t had sleep for four days, people are so frightened; it’s just been a nightmare it really has.”
The Indonesian Red Cross nevertheless reported that they had helped a woman give birth at a temporary healthcare station in the direct aftermath of the earthquake.
Writing on Twitter, they said: “An Indonesian Red Cross volunteer helped Sri Handayani give birth to her new born baby.
“She gave birth at the health post in Bayan, north Lombok.”
The child was named Muhammad Gempa Rizki, and the word “Gempa” means earthquake.