diff --git a/src/rulesets/Base/mapreduce.jl b/src/rulesets/Base/mapreduce.jl
index 33eae96d1..9a8e84834 100644
--- a/src/rulesets/Base/mapreduce.jl
+++ b/src/rulesets/Base/mapreduce.jl
@@ -48,3 +48,17 @@ function rrule(
     end
     return y, sum_abs2_pullback
 end
+
+####
+#### prod
+####
+
+function rrule(::typeof(prod), x::AbstractArray{T}; dims=:) where {T<:CommutativeMulNumber}
+    y = prod(x; dims=dims)
+    function prod_pullback(ȳ)
+        # broadcasting the two works out the size no-matter `dims`
+        x̄ = y .* ȳ ./ x
+        return (NO_FIELDS, x̄)
+    end
+    return y, prod_pullback
+end
diff --git a/test/rulesets/Base/mapreduce.jl b/test/rulesets/Base/mapreduce.jl
index 8e53ffdec..abecbc05d 100644
--- a/test/rulesets/Base/mapreduce.jl
+++ b/test/rulesets/Base/mapreduce.jl
@@ -20,4 +20,11 @@
             end
         end
     end  # sum abs2
+
+    @testset "prod" begin
+        test_rrule(prod, randn(5))
+        test_rrule(prod, randn(5, 6))
+        test_rrule(prod, randn(5, 6); fkwargs=(;dims=2))
+        test_rrule(prod, randn(5, 6); fkwargs=(;dims=1))
+    end
 end