The tragedy was discovered after reports of the injured man being struck by a vehicle near a supermarket in Queensland's southeast.
The man with neck wounds was hit in Logan, about 30km south of Brisbane, on Thursday morning.
Police were trying to reach the man's next of kin when officers discovered the bodies of a 38-year-old woman and her one-year-old daughter in the family's nearby home.
Both died from critical injuries from an edged weapon, Detective Superintendent Chris Ahearn said.
"We believe the three of these people live in a family unit at that house - child, mother and father," Det Ahearn said.
"Our investigations are focusing heavily on the nature of their relationship and living arrangements at that house."
Witnesses raised the alarm after seeing a man covered in blood running along a footpath before he was hit by a black utility about 300m from the family home.
Evidence markers have been placed along the footpath, marking a trail of blood leading from the house.
The man remains in a serious condition and is under police guard in hospital.
There were no domestic violence orders involving the couple, police said, adding there was no further threat to the community.
The home remains a crime scene as detectives appeal for anyone with information or dashcam footage to contact police.
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