diff --git a/base/gmp.jl b/base/gmp.jl
index 5d3cabac87e40..8e0c51e6259d6 100644
--- a/base/gmp.jl
+++ b/base/gmp.jl
@@ -668,8 +668,12 @@ function prod(arr::AbstractArray{BigInt})
     # to account for the rounding to limbs in MPZ.mul!
     # (BITS_PER_LIMB-1 would typically be enough, to which we add
     # 1 for the initial multiplication by init=1 in foldl)
-    nbits = GC.@preserve arr sum(arr; init=BITS_PER_LIMB) do x
-        abs(x.size) * BITS_PER_LIMB - leading_zeros(unsafe_load(x.d))
+    nbits = BITS_PER_LIMB
+    for x in arr
+        iszero(x) && return zero(BigInt)
+        xsize = abs(x.size)
+        lz = GC.@preserve x leading_zeros(unsafe_load(x.d, xsize))
+        nbits += xsize * BITS_PER_LIMB - lz
     end
     init = BigInt(; nbits)
     MPZ.set_si!(init, 1)
diff --git a/test/gmp.jl b/test/gmp.jl
index 1125f57b195b3..be11c70e5064f 100644
--- a/test/gmp.jl
+++ b/test/gmp.jl
@@ -227,6 +227,7 @@ let a, b
     @test 0 == sum(BigInt[]) isa BigInt
     @test prod(b) == foldl(*, b)
     @test 1 == prod(BigInt[]) isa BigInt
+    @test prod(BigInt[0, 0, 0]) == 0 # issue #46665
 end
 
 @testset "Iterated arithmetic" begin