Declan Murphy, 41, and his wife Lindsay, 37, had been out with their two young children celebrating their anniversary when a neighbour called to say the house was ablaze.
The fire tore through the bedroom and roof of the family's semi-detached home in Twickenham, London, causing an estimated £250,000 damage.
The family's pet Jack Russell terrier Chilli was rescued by firefighters but died in Declan's arms 30 minutes later from the effects of smoke.
Investigators believe the fire started in seven-year-old Kyra's bedroom when sunbeams focused by a glass jar on a window-sill containing the brightly-coloured bands caused a dolls' house to burst into flames.
The Murphys, with three-year-old son Coen, have been staying in a hotel since the blaze on February 15 but hope to move back into a rented house in the street later this week.
Declan told his local paper: "They think part of the glass edge of the Nutella jar caught the sun and turned it into a magnifying glass.
"The light was focused on part of the floor that had a dolls' house which caught fire and flames spread to the roof.
"We got home and there was smoke pouring out of the roof and there were four fire engines and police outside.
"It was surreal. I was dumbfounded and I'm still waiting for the sledgehammer of shock to hit me.
"We have lost everything bar the shirts on our backs."
Declan said: "We had Chilli for nine-years and she was part of the family. I held her for 30 minutes in the back of the fire engine. It was heart breaking."
London Fire Brigade investigator Charlie Pugsley said: "It sounds far fetched that a jar containing a few rubber bands caused a severe house fire but that's exactly what happened.
Declan added: "Kyra was inconsolable and blamed herself but we had to tell her that it was an accident and not her fault at all.
"The other day someone gave me a bag of Loom bands to give to her as a replacement. They went straight in the bin. Too many bad memories."