diff --git a/backend.native/compiler/ir/backend.native/src/org/jetbrains/kotlin/backend/konan/objcexport/ObjCExportHeaderGenerator.kt b/backend.native/compiler/ir/backend.native/src/org/jetbrains/kotlin/backend/konan/objcexport/ObjCExportHeaderGenerator.kt
index f4fa2a9e5fd..450ab348685 100644
--- a/backend.native/compiler/ir/backend.native/src/org/jetbrains/kotlin/backend/konan/objcexport/ObjCExportHeaderGenerator.kt
+++ b/backend.native/compiler/ir/backend.native/src/org/jetbrains/kotlin/backend/konan/objcexport/ObjCExportHeaderGenerator.kt
@@ -949,6 +949,12 @@ abstract class ObjCExportHeaderGenerator internal constructor(
         add("#pragma clang diagnostic push")
         listOf(
                 "-Wunknown-warning-option",
+
+                // Protocols don't have generics, classes do. So generated header may contain
+                // overriding property with "incompatible" type, e.g. `Generic<T>`-typed property
+                // overriding `Generic<id>`. Suppress these warnings:
+                "-Wincompatible-property-type",
+
                 "-Wnullability"
         ).forEach {
             add("#pragma clang diagnostic ignored \"$it\"")
diff --git a/backend.native/tests/objcexport/expectedLazy.h b/backend.native/tests/objcexport/expectedLazy.h
index a233bc6e11c..5cbcfc4a04e 100644
--- a/backend.native/tests/objcexport/expectedLazy.h
+++ b/backend.native/tests/objcexport/expectedLazy.h
@@ -204,6 +204,33 @@ __attribute__((swift_name("GH4002Argument")))
 + (instancetype)new __attribute__((availability(swift, unavailable, message="use object initializers instead")));
 @end;
 
+__attribute__((objc_subclassing_restricted))
+__attribute__((swift_name("TestIncompatiblePropertyTypeWarning")))
+@interface KtTestIncompatiblePropertyTypeWarning : KtBase
+- (instancetype)init __attribute__((swift_name("init()"))) __attribute__((objc_designated_initializer));
++ (instancetype)new __attribute__((availability(swift, unavailable, message="use object initializers instead")));
+@end;
+
+__attribute__((objc_subclassing_restricted))
+__attribute__((swift_name("TestIncompatiblePropertyTypeWarningGeneric")))
+@interface KtTestIncompatiblePropertyTypeWarningGeneric<T> : KtBase
+- (instancetype)initWithValue:(T _Nullable)value __attribute__((swift_name("init(value:)"))) __attribute__((objc_designated_initializer));
+@property (readonly) T _Nullable value __attribute__((swift_name("value")));
+@end;
+
+__attribute__((swift_name("TestIncompatiblePropertyTypeWarningInterfaceWithGenericProperty")))
+@protocol KtTestIncompatiblePropertyTypeWarningInterfaceWithGenericProperty
+@required
+@property (readonly) KtTestIncompatiblePropertyTypeWarningGeneric<id> *p __attribute__((swift_name("p")));
+@end;
+
+__attribute__((objc_subclassing_restricted))
+__attribute__((swift_name("TestIncompatiblePropertyTypeWarning.ClassOverridingInterfaceWithGenericProperty")))
+@interface KtTestIncompatiblePropertyTypeWarningClassOverridingInterfaceWithGenericProperty : KtBase <KtTestIncompatiblePropertyTypeWarningInterfaceWithGenericProperty>
+- (instancetype)initWithP:(KtTestIncompatiblePropertyTypeWarningGeneric<NSString *> *)p __attribute__((swift_name("init(p:)"))) __attribute__((objc_designated_initializer));
+@property (readonly) KtTestIncompatiblePropertyTypeWarningGeneric<NSString *> *p __attribute__((swift_name("p")));
+@end;
+
 __attribute__((objc_subclassing_restricted))
 __attribute__((swift_name("Kt35940Kt")))
 @interface KtKt35940Kt : KtBase
diff --git a/backend.native/tests/objcexport/headerWarnings.kt b/backend.native/tests/objcexport/headerWarnings.kt
new file mode 100644
index 00000000000..7894eeccd33
--- /dev/null
+++ b/backend.native/tests/objcexport/headerWarnings.kt
@@ -0,0 +1,18 @@
+/*
+ * Copyright 2010-2020 JetBrains s.r.o. Use of this source code is governed by the Apache 2.0 license
+ * that can be found in the LICENSE file.
+ */
+
+package headerWarnings
+
+// Note: the test parses the generated header with -Werror to detect warnings.
+
+class TestIncompatiblePropertyTypeWarning {
+    class Generic<T>(val value: T)
+
+    interface InterfaceWithGenericProperty<T> {
+        val p: Generic<T>
+    }
+
+    class ClassOverridingInterfaceWithGenericProperty(override val p: Generic<String>) : InterfaceWithGenericProperty<String>
+}
diff --git a/backend.native/tests/objcexport/headerWarnings.swift b/backend.native/tests/objcexport/headerWarnings.swift
new file mode 100644
index 00000000000..afd0064b9d6
--- /dev/null
+++ b/backend.native/tests/objcexport/headerWarnings.swift
@@ -0,0 +1,31 @@
+/*
+ * Copyright 2010-2020 JetBrains s.r.o. Use of this source code is governed by the Apache 2.0 license
+ * that can be found in the LICENSE file.
+ */
+
+import Kt
+
+// Note: the test parses the generated header with -Werror to detect warnings.
+// It is enough to have just Kotlin declarations at the moment.
+// Adding usages for all declarations to avoid any kind of DCE that may appear later.
+
+private func testIncompatiblePropertyType() throws {
+    let c = TestIncompatiblePropertyTypeWarning.ClassOverridingInterfaceWithGenericProperty(
+            p: TestIncompatiblePropertyTypeWarningGeneric<NSString>(value: "cba")
+    )
+
+    let pc: TestIncompatiblePropertyTypeWarningGeneric<NSString> = c.p
+    try assertEquals(actual: pc.value, expected: "cba")
+
+    let i: TestIncompatiblePropertyTypeWarningInterfaceWithGenericProperty = c
+    let pi: TestIncompatiblePropertyTypeWarningGeneric<AnyObject> = i.p
+    try assertEquals(actual: pi.value as! String, expected: "cba")
+}
+
+class HeaderWarningsTests : SimpleTestProvider {
+    override init() {
+        super.init()
+
+        test("TestIncompatiblePropertyType", testIncompatiblePropertyType)
+    }
+}
\ No newline at end of file