The club said it had taken the decision as a result of "complexities linked to the planned game" in Abuja on 5 August.
"We could not get comfortable on everything needed to satisfy our requirements," said Arsenal marketing director Angus Kinnear.
The club are now planning to visit the country next year instead.
In a statement on the Arsenal website, Kinnear added: "Bringing a top-level club to an international market is always complicated and logistically challenging.
"With the proposed match in Nigeria planned for early August, we could not get comfortable on everything needed to satisfy our requirements, so we have reluctantly taken the decision to postpone the team's visit.
"We have a huge and loyal following in Africa, and we are sorry that the team will not be visiting this summer. However, we have a long-term commitment to Nigeria."