The North London club had planned to visit the African nation for the first time in 19 years for a match against Nigeria in Abuja on August 5.
"Bringing a top-level club to an international market is always complicated and logistically challenging," Arsenal marketing director Angus Kinnear said in a statement on the club's website.
"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."
Kinnear said the club were making plans to visit Nigeria next summer.
Islamist group Boko Haram has been fighting a low-level insurgency in Nigeria for more than two years.
Although its attacks are mostly in the north of Africa's most populous nation it has bombed several targets in the capital Abuja, located in the centre of the country.
Arsenal are due to play three games in Asia, starting in Kuala Lumpur on July 24.
They face Premier League champions Manchester City in the inaugural 'China Cup' in the Bird's Nest stadium in Beijing on July 27 before concluding their tour with a match against Hong Kong champions Kitchee FC.