Per the source, the Bills are proceeding as if the concussion, which was termed "serious," could be career-ending.
Kolb will undergo a battery of tests and the Bills do not want to rush him back even if he can continue his career, the source told Schefter.
While diving for a first down in Saturday's game, Kolb was kneed in the helmet by a Redskins defender. He remained on the field for the final four plays of the drive before departing for the locker room with what the team called concussion-like symptoms.
Kolb, who turned 29 on Saturday, missed time in 2010 and 2012 with concussions, a history that has the Bills concerned.
The Bills are already without rookie EJ Manuel, who underwent a minor procedure on his left knee last week.
Information from ESPN.com's Mike Rodak was used in this report.