The ruckman has been sent for scans to assess the damage, with the Blues to release an injury update on Tuesday.
Pittonet has played ten games this season, averaging 10.1 disposals and 29.2 hitouts per game, bringing his career tally to 51 since his debut in 2016.
The 26-year-old inked a new four-year deal with the Blues last week, committing to the club until at least the end of 2027.
Pittonet's setback is the latest for the Blues, who contended with injury concerns throughout Friday night's 26-point loss.
Patrick Cripps rolled his ankle but is expected to feature against Melbourne this week, but will have to get through training, while both Nic Newman (hamstring) and George Hewett (concussion) won't feature in the Round 12 clash at the MCG.
Ollie Hollands meanwhile will reportedly be sidelined for at least the medium term after suffering an AC joint injury.