Operation Spittlemoor ran from Tuesday to Thursday in Great Horton, an area of Bradford which becomes a hub of activity and celebration during the Islamic festival.
Eleven vehicles were seized for no insurance, while eight were believed to have been used in crime.
The arrests were for a range of offences, including breach of bail, drugs offences, assault, theft of a motor vehicle and being over the prescribed limit.
One man was arrested when a quantity of drugs was seized from a vehicle stopped and searched by Roads Policing officers.
The police also issued twelve notices for anti-social vehicle use. The Section 59 notices give police the power to seize the vehicle if it causes further nuisance.
Eleven motorists were given fixed penalty notices and a total of 30 reports were made for traffic offences.
Bradford Council wardens also issued 47 fixed penalty notices for illegal parking.
Road closures were in place around the area to restrict traffic using Great Horton Road during the busiest times.
Inspector Tom Casey, who leads the Bradford West Neighbourhood Policing Team, said: "I would again like to thank our partners and the Great Horton community for their support and their patience during the road closures.
“The vast majority of people who attended the area for the celebrations caused no issues for ourselves or our partners, and the feedback from residents and councillors has been positive.”
Councillor Abdul Jabar, Bradford Council Executive Member for Neighbourhoods and Community Safety, said: “Everyone deserves to be able to live in a safe environment and celebrate festivities such as Eid appropriately.
“Anyone who drives at excessive speeds, use a mobile device whilst driving, drives in an anti-social, careless or dangerous manner at any time of the year is likely to face fines, penalty points and risk having their vehicles seized. “We have to do all we can to reduce the number of road collisions and casualties across the whole district.”