Following an incident on Good Friday, Reeves, whose real name is Jim Moir, was arrested and charged with drink-driving and leaving the scene of an accident.
After details of Reeves' arrest broke in the national press, Churchill decided to pull its current TV ads, which feature his voice. It is now deciding whether to drop the comedian altogether.
A Churchill spokeswoman said the company took road safety very seriously and was reviewing the situation as it was 'extremely concerned' about the incident.
Reeves has provided the voice of the nodding dog brand icon in Churchill's ads for nine years.