A man is fighting for his life and a child has been injured after they were hit by a car outside The Glen shopping centre in Melbourne's south-east.

The female driver stopped to help after hitting the man and boy at the Springvale Road and O'Sullivan Road intersection in Glen Waverley about 6.50am on Tuesday.

The man was taken to The Alfred hospital in a critical condition with head injuries.

The boy has arm injuries and was taken to the Monash Medical Centre in a stable condition.