diff --git a/conan/tools/cmake/cmake.py b/conan/tools/cmake/cmake.py
--- a/conan/tools/cmake/cmake.py
+++ b/conan/tools/cmake/cmake.py
@@ -147,6 +147,10 @@ def install(self, build_type=None, component=None):
         arg_list = ["--install", build_folder, build_config, "--prefix", pkg_folder]
         if component:
             arg_list.extend(["--component", component])
+
+        do_strip = self._conanfile.conf.get("tools.cmake:install_strip", check_type=bool)
+        if do_strip:
+            arg_list.append("--strip")
         arg_list = " ".join(filter(None, arg_list))
         command = "%s %s" % (self._cmake_program, arg_list)
         self._conanfile.output.info("CMake command: %s" % command)

diff --git a/conans/test/unittests/tools/cmake/test_cmake_install.py b/conans/test/unittests/tools/cmake/test_cmake_install.py
--- a/conans/test/unittests/tools/cmake/test_cmake_install.py
+++ b/conans/test/unittests/tools/cmake/test_cmake_install.py
@@ -31,9 +31,38 @@ def test_run_install_component():
     conanfile.settings = settings
     conanfile.folders.set_base_package(temp_folder())
 
-    # Choose generator to match generic setttings
+    # Choose generator to match generic settings
     write_cmake_presets(conanfile, "toolchain", "Visual Studio 14 2015", {})
     cmake = CMake(conanfile)
     cmake.install(component="foo")
 
     assert "--component foo" in conanfile.command
+
+
+def test_run_install_strip():
+    """
+    Testing that the install/strip rule is called
+    Issue related: https://github.com/conan-io/conan/issues/14166
+    """
+
+    settings = Settings.loads(get_default_settings_yml())
+    settings.os = "Linux"
+    settings.arch = "x86_64"
+    settings.build_type = "Release"
+    settings.compiler = "gcc"
+    settings.compiler.version = "11"
+
+    conanfile = ConanFileMock()
+
+    conanfile.conf = Conf()
+    conanfile.conf["tools.cmake:install_strip"] = True
+
+    conanfile.folders.generators = "."
+    conanfile.folders.set_base_generators(temp_folder())
+    conanfile.settings = settings
+    conanfile.folders.set_base_package(temp_folder())
+
+    write_cmake_presets(conanfile, "toolchain", "Unix Makefiles", {})
+    cmake = CMake(conanfile)
+    cmake.install()
+    assert "--strip" in conanfile.command

[feature] Add '--strip' option to cmake install
### What is your suggestion?

Can you add a parameter to `cmake.install` function in order to be able to strip binaries before install ?

install and strip were added to CMake about 4 years ago, and if I got it correctly in version 3.15
https://gitlab.kitware.com/cmake/cmake/-/merge_requests/3069

Strip is very useful to remove debug symbols (actually all DWARF extension) from binaries and especially release binaries.

I tried many options to make it work with conan, but without success, so I think adding this option as a parameter to `install` function in `cmake` tool will be the best solution instead of some workarounds.

### Have you read the CONTRIBUTING guide?

- [X] I've read the CONTRIBUTING guide

conans/test/unittests/tools/cmake/test_cmake_install.py::test_run_install_strip
conans/test/unittests/tools/cmake/test_cmake_install.py::test_run_install_component