diff --git a/src/dense.jl b/src/dense.jl
index ccf6bc80..234391e5 100644
--- a/src/dense.jl
+++ b/src/dense.jl
@@ -972,7 +972,8 @@ sqrt(::AbstractMatrix)
 function sqrt(A::AbstractMatrix{T}) where {T<:Union{Real,Complex}}
     if checksquare(A) == 0
         return copy(float(A))
-    elseif isdiag(A)
+    elseif isdiag(A) && (T <: Complex || all(x -> x ≥ zero(x), diagview(A)))
+        # Real Diagonal sqrt requires each diagonal element to be positive
         return applydiagonal(sqrt, A)
     elseif ishermitian(A)
         sqrtHermA = sqrt(Hermitian(A))
diff --git a/test/dense.jl b/test/dense.jl
index 1f953ea9..1d4b330c 100644
--- a/test/dense.jl
+++ b/test/dense.jl
@@ -984,6 +984,12 @@ end
 @testset "sqrt for diagonal" begin
     A = diagm(0 => [1, 2, 3])
     @test sqrt(A)^2 ≈ A
+
+    A = diagm(0 => [1.0, -1.0])
+    @test sqrt(A) == diagm(0 => [1.0, 1.0im])
+    @test sqrt(A)^2 ≈ A
+    B = im*A
+    @test sqrt(B)^2 ≈ B
 end
 
 @testset "issue #40141" begin