The 27-year-old defender and team-mates Claude Davis and Kyle McFadzean have also been fined two weeks' wages following the ugly scenes at the end of the League Two match on March 27.
A statement on Crawley's website read: "Pablo Mills has been stripped of the captaincy. Crawley Town did not consider his actions befitting that of a club captain.
"The reputation of Crawley Town FC as a welcoming, family club is paramount to out ongoing strategy of development and we will not tolerate incidents such as that at Bradford."
Mills and Davis together with Bradford's Jon McLaughlin, Andrew Davies and Luke Oliver were all sent off after a mass punch-up at the final whistle and are currently suspended
McFadzean has since been banned for three matches by the Football Association while Mills is facing an additional FA violent conduct charge.