Sam suffered the injury in a tackle from Millers defender Shaun Barker, who was shown a yellow card for the offence.
The summer signing, who joined from Wrexham, had made just two appearances from the bench for the Valiants.
It means the Valiants are now withouth seven first team players through injury.
Robin Hulbert, Mark Innes, Michael Walsh to injury are all currently receiving treatment - while George Abbey, Mickey Bell and Sam Collins also picked up knocks against Rotherham.