diff --git a/base/reduce.jl b/base/reduce.jl
index 414bac5099f78..6d19fa50e3037 100644
--- a/base/reduce.jl
+++ b/base/reduce.jl
@@ -306,25 +306,29 @@ with reduction `op` over an empty array with element type of `T`.
 
 If not defined, this will throw an `ArgumentError`.
 """
-reduce_empty(op, T) = _empty_reduce_error()
-reduce_empty(::typeof(+), T) = zero(T)
+reduce_empty(op, ::Type{T}) where {T} = _empty_reduce_error()
+reduce_empty(::typeof(+), ::Type{Union{}}) = _empty_reduce_error()
+reduce_empty(::typeof(+), ::Type{T}) where {T} = zero(T)
 reduce_empty(::typeof(+), ::Type{Bool}) = zero(Int)
-reduce_empty(::typeof(*), T) = one(T)
+reduce_empty(::typeof(*), ::Type{Union{}}) = _empty_reduce_error()
+reduce_empty(::typeof(*), ::Type{T}) where {T} = one(T)
 reduce_empty(::typeof(*), ::Type{<:AbstractChar}) = ""
 reduce_empty(::typeof(&), ::Type{Bool}) = true
 reduce_empty(::typeof(|), ::Type{Bool}) = false
 
-reduce_empty(::typeof(add_sum), T) = reduce_empty(+, T)
+reduce_empty(::typeof(add_sum), ::Type{Union{}}) = _empty_reduce_error()
+reduce_empty(::typeof(add_sum), ::Type{T}) where {T} = reduce_empty(+, T)
 reduce_empty(::typeof(add_sum), ::Type{T}) where {T<:SmallSigned}  = zero(Int)
 reduce_empty(::typeof(add_sum), ::Type{T}) where {T<:SmallUnsigned} = zero(UInt)
-reduce_empty(::typeof(mul_prod), T) = reduce_empty(*, T)
+reduce_empty(::typeof(mul_prod), ::Type{Union{}}) = _empty_reduce_error()
+reduce_empty(::typeof(mul_prod), ::Type{T}) where {T} = reduce_empty(*, T)
 reduce_empty(::typeof(mul_prod), ::Type{T}) where {T<:SmallSigned}  = one(Int)
 reduce_empty(::typeof(mul_prod), ::Type{T}) where {T<:SmallUnsigned} = one(UInt)
 
-reduce_empty(op::BottomRF, T) = reduce_empty(op.rf, T)
-reduce_empty(op::MappingRF, T) = mapreduce_empty(op.f, op.rf, T)
-reduce_empty(op::FilteringRF, T) = reduce_empty(op.rf, T)
-reduce_empty(op::FlipArgs, T) = reduce_empty(op.f, T)
+reduce_empty(op::BottomRF, ::Type{T}) where {T} = reduce_empty(op.rf, T)
+reduce_empty(op::MappingRF, ::Type{T}) where {T} = mapreduce_empty(op.f, op.rf, T)
+reduce_empty(op::FilteringRF, ::Type{T}) where {T} = reduce_empty(op.rf, T)
+reduce_empty(op::FlipArgs, ::Type{T}) where {T} = reduce_empty(op.f, T)
 
 """
     Base.mapreduce_empty(f, op, T)
diff --git a/test/reduce.jl b/test/reduce.jl
index 69b8b1911e7ea..9501f41f8b77c 100644
--- a/test/reduce.jl
+++ b/test/reduce.jl
@@ -46,6 +46,8 @@ end
 @test reduce(max, [8 6 7 5 3 0 9]) == 9
 @test reduce(+, 1:5; init=1000) == (1000 + 1 + 2 + 3 + 4 + 5)
 @test reduce(+, 1) == 1
+@test_throws ArgumentError reduce(*, ())
+@test_throws ArgumentError reduce(*, Union{}[])
 
 # mapreduce
 @test mapreduce(-, +, [-10 -9 -3]) == ((10 + 9) + 3)
@@ -133,6 +135,7 @@ fz = float(z)
 @test sum(z) === 136
 @test sum(fz) === 136.0
 
+@test_throws ArgumentError sum(Union{}[])
 @test_throws ArgumentError sum(sin, Int[])
 @test sum(sin, 3) == sin(3.0)
 @test sum(sin, [3]) == sin(3.0)