diff --git a/base/reducedim.jl b/base/reducedim.jl
index c473049dd5fa0..ff2b24db740ef 100644
--- a/base/reducedim.jl
+++ b/base/reducedim.jl
@@ -3,7 +3,7 @@
 ## Functions to compute the reduced shape
 
 # for reductions that expand 0 dims to 1
-reduced_index(i::OneTo) = OneTo(1)
+reduced_index(i::OneTo{T}) where {T} = OneTo(one(T))
 reduced_index(i::Union{Slice, IdentityUnitRange}) = oftype(i, first(i):first(i))
 reduced_index(i::AbstractUnitRange) =
     throw(ArgumentError(
diff --git a/test/reducedim.jl b/test/reducedim.jl
index cc07cfff1dad3..93287efc5eb1c 100644
--- a/test/reducedim.jl
+++ b/test/reducedim.jl
@@ -492,3 +492,16 @@ end
 
 @test @inferred(count(false:true, dims=:, init=0x0004)) === 0x0005
 @test @inferred(count(isodd, reshape(1:9, 3, 3), dims=:, init=Int128(0))) === Int128(5)
+
+@testset "reduced_index for BigInt (issue #39995)" begin
+    for T in [Int8, Int16, Int32, Int64, Int128, BigInt]
+        r = T(1):T(2)
+        ax = axes(r, 1)
+        axred = Base.reduced_index(ax)
+        @test axred == Base.OneTo(1)
+        @test typeof(axred) === typeof(ax)
+        r_red = reduce(+, r, dims = 1)
+        @test eltype(r_red) == T
+        @test r_red == [3]
+    end
+end