Nobody was injured when the windows of a Volkswagen Golf were shot out in the restaurant's car park at St Andrews Quay on 2 January.
Humberside Police said the arrested man had been bailed until April.
A number of other people have been arrested over the past few weeks. Police said inquiries were continuing.
Police have arrested a 21-year-old Hull man on suspicion of conspiracy to murder in connection with a shooting incident at a McDonald's in the city.