A woman and a child have been found dead in a home south of Brisbane this morning.

Police were called to a supermarket on Beaudesert Beenleigh Road at Bannockburn, a suburb of Logan, at around 7.30am, where they found a man with injuries.

Officers discovered the man had run to the supermarket from a property at nearby Belivah.

When investigators went to the house at Belivah, they found the bodies of a woman and a child.

The man is receiving medical treatment and will be assisting police with their investigations.

Police do not believe there is any ongoing threat to the community.