The England international was with his Hammers team-mates in Dublin for a weekend Christmas party following his side's 3-1 win over Chelsea.
Officers received a report of an incident at 02.30GMT on Monday, according to a spokesman for the Garda press office in Dublin, where a photographer claimed that he was assaulted in the city's main shopping district, Grafton Street.
Police are continuing to investigate the incident and West Ham players have been spoken to but no arrests were made, according to a spokesman for the club.
"Andy Carroll was in Dublin as part of a social trip with full permission of the management team," a statement said.
"Andy agreed to have a number of pictures taken at the request of a photographer who was waiting on the street. Despite this, the photographer then carried on taking photos in the close proximity of Andy and was politely asked to stop by the private security team working on the trip.
"When he then continued taking more photos he was restrained by the security team for Andy's safety. Eyewitnesses state at no point was there any physical contact between Andy and the photographer."