Police and Yorkshire Electricity staff are investigating the accident which killed Cara Weatherstone in Hornsea, East Yorkshire.
Her parents, Beverley, 38, and Anthony, 40, and six brothers and sisters, aged between 15 months and 18, were all with her in the living-room when it happened, on Saturday.
It is understood that Cara stood with her bare foot on a copper gas pipe running round the room to switch on the lights, which were plugged into a table lamp.
As she turned the switch, she received a shock which probably killed her instantly.
The family had put up the fir tree last week and Cara had switched on the lights on previous occasions. The investigation will centre on whether there was a fault with the arrangement or with the way they were wired.
"It all so happened so quickly," George Weatherstone, her 67-year-old grandfather, said yesterday.
"The current grabbed Cara. Her sister Fiona tried to push her off and got a tingle herself and then Cara fell off. The whole family saw it, but could do nothing."
Police and ambulance were called but Cara, a pupil at Hornsea Infants School, was pronounced dead on arrival at Hull Royal Infirmary.
Mr Weatherstone said that Cara's father, his son - who works for East Riding Social Services - and her mother were devastated.
"Anthony and Beverley are in a terrible state. It's such a tragedy," he said.
"Poor little Cara. She had turned the lights on so many times before, it was just unfortunate that she had her bare foot on the gas pipe. She was earthed and could not be thrown off by the electric shock."
A Humberside police spokeswoman said: "Extensive inquiries revealed that the incident appeared to have been a tragic accident."