The incident happened at the Waterside Theatre on Friday.
Primary-school aged children were attending the event as part of a summer scheme.
The image of a partially undressed woman appeared on screen for several seconds before being removed.
The theatre has apologised and described the incident as “unfortunate but serious”.
In a post on Facebook on Friday night, staff said they would be “working with the relevant authorities”.
Parents of the children who attended the screening were informed of the incident by organisers soon after it happened before police were alerted.
A PSNI spokesperson said they had received a report of an indecent image appearing briefly on the screen and had begun an investigation.
“Enquiries remain ongoing and anyone with information that could help with this investigation is asked to contact police,” they added.
In a Facebook post on Friday, the arts centre said: “Waterside Theatre is aware of an unfortunate but serious incident happening today.
“The welfare of our visitors is always our main concern and we will be working with the relevant authorities,” the statement goes on.
“We offer or sincere apologies to all those affected.”
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