Clarke, who led his side to a 2-1 test series victory over South Africa, was struck on the left shoulder during the third test in Cape Town earlier this month yet still went on to make 161 not out in the tourists' first innings.
"We have since done a series of scans that have demonstrated a fracture near his shoulder joint," Australian team physiotherapist Alex Kountouris said in a statement.
"We expect that this will heal with a period of rest."
Clarke's New South Wales team will play Western Australia in the domestic Sheffield Shield final in Canberra from March 21-25.
Clarke, who was also struck in the arm, thumb, elbow and helmet in the Cape Town match, was due a long break away from the game anyway as he was not in Australia's squad for the ongoing World Twenty20 tournament in Bangladesh.
The 32-year-old made himself unavailable for the shortest form of the game at international level in 2011.
Australia's next international series is against Pakistan, probably in the United Arab Emirates, in October.
(Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien)
