The on-loan Leicester defender was sent off for two bookable offences as Albion began their League Two campaign with a 2-2 draw at last season's play-off finalists Torquay on Saturday.
Parkes will serve a one-match suspension but boss Paul Peschisolido is confident he has enough central defensive cover at his disposal.
"We've got a good set of lads at the club," said the Canadian. "We've got Tony James and Ryan Austin, and Darren Moore is coming back to fitness, so we'll be alright."
Midfielder Jimmy Phillips and striker Greg Pearson will hope for starts after having to settle for substitute roles at the weekend.