The 28-year-old was struck by a ball hit by Sydney Sixers team mate Michael Lumb in the nets on Monday ahead of their Big Bash semi-final against Brisbane, which takes place later on Wednesday.
"After being struck on the head by a ball at training on Monday, Joe was transported to a hospital in Brisbane where he underwent a series of check-ups before being discharged later that evening," CA's Chief Medical Officer John Orchard said in a statement.
"Joe was reviewed by a Cricket Australia doctor on Tuesday and had some scans performed that revealed a small fracture and associated minor brain bleed.
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"Whilst this is a serious injury, Joe is feeling well. We believe that this is a stable injury and will not require surgery."
Mennie, who made his test debut for Australia against South Africa last November, remained in hospital under the care of a neurosurgeon for observation, Orchard added.
(Writing by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
