Two of the people being treated in hospital are believed to have lived at the house, the BBC understands.
Avon and Somerset Police said their injuries are not believed to be life-threatening or life-changing.
"A fourth person has sustained minor injuries and was seen by the ambulance service," the force added.
A cordon remains in place and members of the public are being advised to avoid the area while emergency services are at the scene.
Rich Cainey has lived next door to the damaged property with his parents for 35 years.
He told the BBC he was asleep when he was suddenly "thrown out of bed" by the impact of the explosion.
"I ran outside and saw next door's house was completely gone and engulfed in flames," said Mr Cainey.
"I could hear screams from next door so my first thought was to get everyone out safely."
He said that his father – a former police officer – was walking their dogs when the explosion happened and rushed into the building to help the occupants out.
"It was instant panic from all the neighbours, everyone was running around in the street," Mr Cainey continued.
"No one was really thinking about anything but making sure everyone was safe."
The Avon Fire and Rescue Service said the blaze has since been "safely extinguished".
"We were called at 06:53 BST this morning to reports of a gas explosion in a residential home on Lancaster Road, Yate," it added in a statement.
"The explosion caused a fire, which has now been safely extinguished. A cordon has been put in place.
"Local people are asked to avoid the area while we deal with the incident."
