By definition, space militarization is the placement and development of weapons and military technology in Earth orbits. Although ballistic missiles do transit space, they do not stay in space. Therefore, such missiles are not considered to be space weapons.
It is true that space is the home of many devices that serve national security interests. For example, there are many imaging and communications satellites that are owned and operated by defense and security organizations of governments. However, these are thought to be weaponless.
Based on publically available information, weapons are not currently stationed in space. In fact, the Outer Space Treaty, the basic legal framework of international space law, bars any signatory to the treaty from placing weapons of mass destruction in orbit, installing them on the Moon or any other celestial body.
On the other hand, the Treaty does not prohibit the placement of conventional weapons in orbit. Accordingly, governments are forbidden from claiming ownership of celestial resources such as the Moon or a planet.
Full article: Weapons in Space (Spacewar)