The Canadian international turned his ankle yesterday morning and will have the joint scanned in the next 24 hours.
The Rangers medical team have confirmed that there appears to be some ligament damage, but it may be insignificant enough to sideline the player for no more than two weeks.
Bircham only joined up with the rest of the squad for pre-season training this week having been given extra time off following his international stint with Canada.
Now he will begin a rehab programme that will hopefully ensure his availability for the friendlies against Bristol Rovers and Crystal Palace at the end of the month.
Elsewhere, Dan Shittu and Nick Culkin have both trained with the first team squad and only Richard Edghill was missing yesterday, due to a slight thigh strain.
Rangers' begin their pre-season fixtures with a friendly against Highland Premier League outfit Nairn County on Wednesday evening.
Ian Holloway's team then take on last season's First Division champions Inverness Caledonian Thistle, before returning to England at the weekend.