diff --git a/stdlib/SparseArrays/src/linalg.jl b/stdlib/SparseArrays/src/linalg.jl
index d24cfaf0849a3..c9d25c58750bd 100644
--- a/stdlib/SparseArrays/src/linalg.jl
+++ b/stdlib/SparseArrays/src/linalg.jl
@@ -174,6 +174,10 @@ function (*)(A::AbstractSparseMatrixCSC, D::Diagonal)
     T = Base.promote_op(*, eltype(D), eltype(A))
     mul!(LinearAlgebra.copy_oftype(A, T), A, D)
 end
+function (/)(A::AbstractSparseMatrixCSC, D::Diagonal)
+    T = typeof(oneunit(eltype(A))/oneunit(eltype(D)))
+    rdiv!(LinearAlgebra.copy_oftype(A, T), D)
+end
 
 # Sparse matrix multiplication as described in [Gustavson, 1978]:
 # http://dl.acm.org/citation.cfm?id=355796
diff --git a/stdlib/SparseArrays/test/sparse.jl b/stdlib/SparseArrays/test/sparse.jl
index 3961d0926bca0..5a4bdadcb4398 100644
--- a/stdlib/SparseArrays/test/sparse.jl
+++ b/stdlib/SparseArrays/test/sparse.jl
@@ -519,6 +519,9 @@ dA = Array(sA)
         @test lmul!(Diagonal(bi), copy(dA)) ≈ ldiv!(Diagonal(b), copy(sA))
         @test lmul!(Diagonal(bi), copy(dA)) ≈ ldiv!(transpose(Diagonal(b)), copy(sA))
         @test lmul!(Diagonal(conj(bi)), copy(dA)) ≈ ldiv!(adjoint(Diagonal(b)), copy(sA))
+        Aob = Diagonal(b) \ sA
+        @test Aob == ldiv!(Diagonal(b), copy(sA))
+        @test issparse(Aob)
         @test_throws DimensionMismatch ldiv!(Diagonal(fill(1., length(b)+1)), copy(sA))
         @test_throws LinearAlgebra.SingularException ldiv!(Diagonal(zeros(length(b))), copy(sA))
 
@@ -527,6 +530,9 @@ dA = Array(sA)
         @test rmul!(copy(dAt), Diagonal(bi)) ≈ rdiv!(copy(sAt), Diagonal(b))
         @test rmul!(copy(dAt), Diagonal(bi)) ≈ rdiv!(copy(sAt), transpose(Diagonal(b)))
         @test rmul!(copy(dAt), Diagonal(conj(bi))) ≈ rdiv!(copy(sAt), adjoint(Diagonal(b)))
+        Atob = sAt / Diagonal(b)
+        @test Atob == rdiv!(copy(dAt), Diagonal(b))
+        @test issparse(Atob)
         @test_throws DimensionMismatch rdiv!(copy(sAt), Diagonal(fill(1., length(b)+1)))
         @test_throws LinearAlgebra.SingularException rdiv!(copy(sAt), Diagonal(zeros(length(b))))
     end