Vandals pulled lights off some of the cycles while one was badly damaged by an apparent attempt to wrench it from its stand.
The scheme's sponsors, outdoor advertising giant JC Decaux, will be watching how the scheme fares after widespread vandalism hit a similar initiative in Paris.
Dublin's first bicycle rental scheme was launched yesterday after months of controversy.
Dubliners and tourists got the scheme off to an enthusiastic start with 1,000 cyclists availing of the service by last night.
Dublin City Council received the bicycles free of charge as part of a 'bikes for billboards' deal with JC Decaux.
The scheme came in for criticism because, while the billboards have been in place for the past year, it took until now to provide the bicycles.
There are 450 bikes available for hire at 40 stations scattered across the city centre allowing people to make free short-hop trips of up to half-an-hour.
The busiest stations yesterday were at St Stephen's Green, Smithfield and at Christchurch.
It is hoped that each bike will be used nine times per day, totalling 4,000 journeys.
There have been 2,000 subscriptions so far, and the council expects that total by the end of the week to be 9,000.
Although most of the overnight damage was minor, the bikes have to be repaired to keep them roadworthy.
As well as the vandalised bicycles, some had flat tyres -- but this could be down to punctures or accidents.
In Paris, vandals have plagued that city's otherwise successful "Velib" scheme.