"We believe that this is a stable injury and will not require surgery.
"As a precautionary measure, Joe has been admitted to hospital for observation and will continue to be assessed by a neurosurgeon to determine best course of action."
Mennie was preparing for Wednesday's semi-final against Brisbane Heat when he was struck.
Sixers veteran Brad Haddin described the incident as "scary".
"He was bowling in the nets and (batsman) Michael Lumb got hold of one straight back and he's followed through and got him in the head," Haddin told Sky Sports Radio on Tuesday.
Mennie, who made his Test debut for Australia against South Africa in November, joined the Sixers in April following three summers with Hobart.
He has played just twice for the franchise this season, most recently against the Hurricanes in Sydney on December 23.
- AAP