The 24-year-old promotion-winning keeper sustained the injury after colliding with Altrincham attacker Justin Amaluzor – and was sent off in the process.
Gregory is suspended for Tuesday's trip to Gateshead – but will now be sidelined for an indefinite period regardless.
All at the Jakemans Community Stadium would like to wish the player a speedy recovery, who in turn has thanked the medical staff at Altrincham and those at Wythenshawe Hospital and Manchester Royal Infirmary for their care and attention over the weekend.
Get well soon, Cam!