diff --git a/stdlib/LinearAlgebra/src/LinearAlgebra.jl b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
index 9b9aaf0d9581d..a8c6792178aec 100644
--- a/stdlib/LinearAlgebra/src/LinearAlgebra.jl
+++ b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
@@ -581,6 +581,8 @@ matprod_dest(A::Diagonal, B::StructuredMatrix, TS) = similar(B, TS)
 matprod_dest(A::Diagonal, B::Diagonal, TS) = similar(B, TS)
 matprod_dest(A::HermOrSym, B::Diagonal, TS) = similar(A, TS, size(A))
 matprod_dest(A::Diagonal, B::HermOrSym, TS) = similar(B, TS, size(B))
+# Special handling for adj/trans vec
+matprod_dest(A::Diagonal, B::AdjOrTransAbsVec, TS) = similar(B, TS)
 
 # TODO: remove once not used anymore in SparseArrays.jl
 # some trait like this would be cool
diff --git a/stdlib/LinearAlgebra/test/diagonal.jl b/stdlib/LinearAlgebra/test/diagonal.jl
index 18abc6940eded..3087e87f63415 100644
--- a/stdlib/LinearAlgebra/test/diagonal.jl
+++ b/stdlib/LinearAlgebra/test/diagonal.jl
@@ -1277,4 +1277,15 @@ end
     @test c == Diagonal([2,2,2,2])
 end
 
+@testset "mul/div with an adjoint vector" begin
+    A = [1.0;;]
+    x = [1.0]
+    yadj = Diagonal(A) \ x'
+    @test typeof(yadj) == typeof(x')
+    @test yadj == x'
+    yadj = Diagonal(A) * x'
+    @test typeof(yadj) == typeof(x')
+    @test yadj == x'
+end
+
 end # module TestDiagonal