diff --git a/src/operators.jl b/src/operators.jl
index 8150658fdb2..b1f8d1c1348 100644
--- a/src/operators.jl
+++ b/src/operators.jl
@@ -502,3 +502,32 @@ function _MA.operate!!(
 )
     return _throw_operator_error(op, x)
 end
+
+_mult_upper(α, A) = parent(α * LinearAlgebra.UpperTriangular(parent(A)))
+_mult_lower(α, A) = parent(α * LinearAlgebra.LowerTriangular(parent(A)))
+
+function Base.:*(
+    x::Union{
+        GenericVariableRef{<:Real},
+        GenericAffExpr{<:Real},
+        GenericQuadExpr{<:Real},
+    },
+    A::LinearAlgebra.Hermitian,
+)
+    c = LinearAlgebra.sym_uplo(A.uplo)
+    B = c == :U ? _mult_upper(x, A) : _mult_lower(x, A)
+    # Intermediate conversion to `Matrix` is needed to work around
+    # https://github.com/JuliaLang/julia/issues/52895
+    return LinearAlgebra.Hermitian(Matrix(LinearAlgebra.Hermitian(B, c)), c)
+end
+
+function Base.:*(
+    A::LinearAlgebra.Hermitian,
+    x::Union{
+        GenericVariableRef{<:Real},
+        GenericAffExpr{<:Real},
+        GenericQuadExpr{<:Real},
+    },
+)
+    return x * A
+end
diff --git a/test/test_complex.jl b/test/test_complex.jl
index db61feff447..7b64c027f20 100644
--- a/test/test_complex.jl
+++ b/test/test_complex.jl
@@ -323,4 +323,19 @@ function test_hermitian_jump_scalar()
     return
 end
 
+function test_mul_real_hermitian()
+    A = [1+1im 1+1im; 1-2im 3+1im]
+    model = Model()
+    @variable(model, x)
+    for s in (:L, :U), f in (x, x + 1, x^2)
+        B = LinearAlgebra.Hermitian(A, s)
+        @test f * B isa LinearAlgebra.Hermitian
+        @test isequal_canonical(f * B, LinearAlgebra.Hermitian(f * A, s))
+        @test B * f isa LinearAlgebra.Hermitian
+        @test isequal_canonical(B * f, LinearAlgebra.Hermitian(A * f, s))
+        @test isequal_canonical(f * B + f * B, (2 * f) * B)
+    end
+    return
+end
+
 end  # TestComplexNumberSupport