The program in the borough of Iztapalapa is dubbed "For Your Family: Voluntary Disarmament."
Borough president Jesus Valencia wrote in his Twitter account Monday that residents had turned in 27 rifles and 65 pistols.
The borough has been plagued by violent crime and people firing guns into the air during concerts and celebrations.
In November, 10-year-old Hendrik Cuacuas was hit in the head by a 9-mm bullet during the Disney film "Wreck-It Ralph."
Prosecutors said the round was fired from outside the theater, and spent bullets were found on the roof.