The child was rushed to Christchurch Hospital in a critical condition, but died of her injuries.

A coroner has suppressed the name of a 3-year-old girl killed in a golf club accident while playing with her 7-year-old brother.

Coroner Gordon Matenga told police about the suppression, saying it would be in place until a further court order, Canterbury metro commander Superintendent Lane Todd said.

Emergency services were called to the girl's home in Rolleston, on the outskirts of Christchurch, about 4.10pm Sunday.

Stuff understands the brother accidentally hit the girl in the head with a golf club.

She was rushed to Christchurch Hospital in a critical condition, but died of her injuries.

"We would like to reiterate that the girl's death is not being treated as suspicious and was a tragic accident," Todd said.

"This is already an extremely traumatic time for her family and friends and we urge the community to rally together to support them by respecting their need for privacy at this time."

Todd warned people to be careful about speculating on social media and abide by the Harmful Digital Communications Act 2015.

"The speculation, gossip and conjecture on social media is causing considerable, unnecessary distress to her family and friends," he said.

A family friend said the siblings were "very close" and the "most well mannered, beautiful children".

"You can't get a more loving family. They [the parents] would do anything for those kids, anything at all," she said.

Todd earlier would not discuss the circumstances of the case, but said the family were "traumatised".

He said earlier: "Police understand that she was playing with her 7-year-old sibling at the time of the incident".

The girl's family were receiving support from Police, Victim Support and their family and friends.

"On behalf of Canterbury Police and the members of the emergency services that responded to the address [on Sunday] I would like to pass on our sincere condolences to her family. This incident is even more devastating given that the festive season and summer break are a month away," Todd said.

Stuff decided earlier not to name the family involved to protect the identity of the 7-year-old boy.