diff --git a/src/MArray.jl b/src/MArray.jl
index 9d8e87f3..e1592ee3 100644
--- a/src/MArray.jl
+++ b/src/MArray.jl
@@ -27,16 +27,33 @@ end
     getfield(v,:data)[i]
 end
 
+# copied from `jl_is_layout_opaque`,
+# which is not available for use becaused marked as static inline.
+function is_layout_opaque(@nospecialize(T::DataType))
+    layout = unsafe_load(convert(Ptr{Base.DataTypeLayout}, T.layout))
+    layout.nfields == 0 && layout.npointers > 0
+end
+is_layout_opaque(T) = true
+
 @propagate_inbounds function setindex!(v::MArray, val, i::Int)
     @boundscheck checkbounds(v,i)
     T = eltype(v)
 
     if isbitstype(T)
         GC.@preserve v unsafe_store!(Base.unsafe_convert(Ptr{T}, pointer_from_objref(v)), convert(T, val), i)
+    elseif isconcretetype(T) && ismutabletype(T) && !is_layout_opaque(T)
+        # The tuple contains object pointers.
+        # Replace the pointer at `i` by that of the new mutable value.
+        GC.@preserve v begin
+            data_ptr = Ptr{UInt}(pointer_from_objref(v))
+            value_ptr = Ptr{UInt}(pointer_from_objref(val))
+            unsafe_store!(data_ptr, value_ptr, i)
+        end
     else
-        # This one is unsafe (#27)
-        # unsafe_store!(Base.unsafe_convert(Ptr{Ptr{Nothing}}, pointer_from_objref(v.data)), pointer_from_objref(val), i)
-        error("setindex!() with non-isbitstype eltype is not supported by StaticArrays. Consider using SizedArray.")
+        # For non-isbitstype immutable data, it is safer to replace the whole `.data` field directly after update.
+        # For more context see #27.
+        updated = Base.setindex(v.data, convert(T, val), i)
+        v.data = updated
     end
 
     return v
diff --git a/test/MArray.jl b/test/MArray.jl
index 79022dd9..675c0530 100644
--- a/test/MArray.jl
+++ b/test/MArray.jl
@@ -209,8 +209,30 @@
         @test_throws BoundsError setindex!(mm, 4, 82)
 
         # setindex with non-elbits type
+
         m = MArray{Tuple{2,2,2}, String}(undef)
-        @test_throws ErrorException setindex!(m, "a", 1, 1, 1)
+        @test_throws UndefRefError setindex!(m, "a", 1, 1, 1)
+
+        m = @MArray ["a" "b"; "c" "d"]
+        setindex!(m, "z", 1, 1)
+        @test m[1, 1] == "z"
+        setindex!(m, "y", 1, 2)
+        @test m[1, 2] == "y"
+
+        m = @MArray [[], []]
+        setindex!(m, [2], 2)
+        @test m[2] == [2]
+
+        m = @MArray [Ref([1, 2]), Ref([3, 4])]
+        ref = Ref([5, 6])
+        setindex!(m, ref, 2)
+        @test m[2] === ref
+        ref[] = [7, 8]
+        @test m[2][] == [7, 8]
+
+        m = @MArray Any["a", "b"]
+        setindex!(m, "c", 2)
+        @test m[2] == "c"
     end
 
     @testset "promotion" begin