A distressed kangaroo and its joey were euthanased after the mother was discovered in a Canberra front yard shot with an arrow on Monday.

The ACT Government received several reports from the public about the female kangaroo, which was found outside a home in Hackett.

It was severely injured and was carrying a baby too young to be cared for, an ACT Parks and Conservation Service spokesman said.

He said a ranger acted on veterinary advice in euthanased both animals to prevent further suffering.

The mother appeared to be roughly three years old.

"This is particularly distressing for rangers who have to respond to these incidents and to the community who hear and see these sorts of incidents," the spokesman said.

"Unfortunately PCS receives reports of kangaroos and other native animals shot by arrows, including an emu at the Lower Cotter Catchment about 12 months ago."

The spokesman warned killing, injuring or endangering native animal has maximum penalties of two years in jail and a $75,000 fine.

"Animal cruelty is not tolerated by the community or the Government," he said.

"These are serious offences and whilst all reports are investigated, PCS relies on information from members of the public to identify those persons responsible."

He urged anyone with information about this or similar incidents to contact Crime Stoppers on 1800 333 000.