The injury prone hooker has been diagnosed with a lower neck injury, and club officials fear he may be out for up to three months.
A specialist has advised the 34-year-old to rest over the weekend before a full assessment next week.
Scarlets chief executive Stuart Gallacher said: 'Robin does have a problem, but we are not sure how serious it is just yet.'
The Scarlets face European and Zurich Premiership champions Wasps next Friday.
Their first Celtic League match takes place on 3 September at Borders.
McBryde missed Wales's summer tour to Argentina and South Africa because of a shoulder injury after being a key performer at the World Cup in Australia.
If his injury proves serious, it could leave Wales with a front-row dilemma.
Mefin Davies, who was first-choice hooker in McBryde's absence during the summer, will play his rugby with semi-professional outfit Neath next season, having failed to secure a regional contract.
Huw Bennett, the next in line in the Wales squad, is second-choice hooker at the Ospreys behind Barry Williams - who has retired from international rugby.