Lopez's gig at a luxury hotel had triggered angry protests among Greeks accusing her of according legitimacy to northern Cyprus, a breakaway state recognized only by Ankara.
"Jennifer Lopez would never knowingly support any state, country, institution or regime that was associated with any form of human rights abuse," a statement on Lopez's website said.
"After a full review of the relevant circumstances in Cyprus, it was the decision of her advisors to withdraw from the appearance.
This was a team decision that reflects our sensitivity to the political realities of the region," it said.
Lopez, her husband singer Marc Anthony and their two children were due to stay at the Cratos Premium Hotel, located in a region where thousands of Greek Cypriots were displaced from in 1974. She was booked to perform there on July 24.
"Her fee had been paid and everything was ready, but she felt it was not safe for her to travel. She was led to believe there was a war going on," said Feza Firat, whose Istanbul-based F&F Agency represents Cratos Hotel.
"Several Greek Cypriot families who had made reservations to attend the concert are just as disappointed," she added.
Organizers of the event had this week acknowledged Lopez's publicists were getting thousands of letters of protest, but had assured her Cyprus was safe. A Facebook site against the concert signed up almost 20,000 members within a week.
Cyprus was split in a Turkish invasion which followed a short-lived Greek Cypriot coup engineered by the military junta ruling Greece in 1974. The conflict is one of the longest-standing on the agenda of the United Nations, which is now overseeing peace talks. Incidents of friction have been very limited for decades.
Around 200,000 people, Greek and Turkish Cypriots, were displaced in the 1974 war and ethnic conflict which started in 1963.
(Additional reporting by Ayla Jean Yackley in Istanbul)