An aluminum alloy brazing sheet for heat exchangers, having a core alloy containing Mn 0.6 to 2.0 mass %, Fe 0.05 to 0.5 mass %, Si 0.4 to 0.9 mass %, and Zn 0.02 to 4.0 mass %, with the balance being Al and unavoidable impurities; and as a skin alloy containing Si 6.0 to 13.0 mass %, Fe 0.05 to 0.80 mass %, and Cu 0.05 to 0.45 mass %, with the balance being Al and unavoidable impurities, wherein a ratio A/B of a number density A of specific precipitates with a particle size 0.1 μm or more but less than 3.0 μm, and a number density B of precipitates with a particle size 3.0 μm or more in the core alloy, satisfies: 50≦A/B≦500, and wherein an average grain size of the core alloy in a longitudinal cross-section of a fin after braze-heating is 100 μm or more; and a method of producing the same.