The NFL Commissioner Roger Goodell announced the game had been postponed following the incident, which occurred during the first half.
In a statement, the NFL said: "Hamlin received immediate medical attention on the field by team and independent medical staff and local paramedics.
"He was then transported to a local hospital where he is in a critical condition.
"Our thoughts are with Damar and the Buffalo Bills. We will provide more information as it becomes available.
"The NFL has been in constant communication with the NFL Players Association which is in agreement with postponing the game."
Hamlin's teammates gathered in prayer on the field after witnessing the incident.