The driver of the truck was killed in the blast, and a nine-year-old girl died of cardiac arrest in hospital after succumbing to severe burns, health officials said.
Seven other children were among 33 people hospitalized, some with severe burns, health official Ricardo Sopfi told RPP radio.
Air force helicopters were used to transport the injured to hospitals.
The gas tanker exploded after the truck went over a speed bump as it approached a busy intersection in the Peruvian capital’s Villa El Salvador district.
The resulting blaze engulfed 14 nearby homes, fire department chief Alfonso Panizo told state television.
Firefighters brought the blaze under control after three hours. Others sifted through razed houses in search of survivors or pets