"We know incidents like this are upsetting for our community and we'd like to thank Queenstown residents for the information they have provided to assist our enquiries."
Anyone who has any further information in relation to these incidents or the arrest is asked to contact Queenstown Police on 105.
Six posters depicting offensive images and other hate and sexist material were found around the Queenstown Islamic Centre on Wednesday.
Worshipper Philippe Saint-Pere, who also teaches at the Islamic centre, said the posters were shocking.
"It shows how badly people need to understand what Islam is really all about."
He said when the masjid opened two weeks ago, an event was held for non-Muslims to ask questions about the faith, and around 60 people attended.
Saint-Pere said while he understood the importance of freedom of expression, that did not mean freedom to slander.
