The DF-21 anti ship ballistic missile (https://en.wikipedia.org/wiki/DF-21 https://en.wikipedia.org/wiki/DF-21), affectionately known as the "carrier killer" is

The DF-21 anti ship ballistic missile (https://en.wikipedia.org/wiki/DF-21 https://en.wikipedia.org/wiki/DF-21), affectionately known as the "carrier killer" is capable of maneuvering on the way back down from space, at speeds of mach 5-10. The initial guidance would be through satellites and then final phase guidance through a mix of electro-optical and radar guidance. Carriers, while being fairly fast for a ship, would not have enough time to maneuver away from an incoming missile. It is thought that they might not be able to outright sink a carrier but would inflict enough damage that the carrier would need extensive repairs and be out of the fight for several months at least, and that is for the conventionally armed versions. Nuclear tipped ballistic missiles would melt the ship and anything nearby. US anti ballistic missiles (mostly the SM-3 for naval use) have been tested against ballistic missiles but not (as far as I know) in anything other than a test environment. The launchers are mobile and stationed fairly far inland, specifically to be out of easy reach of naval force projection from a carrier group. Source: Used to be a weapons engineer in the Dutch Navy for 14 years, have been out of it for ~5 years now though. These kind of weapons were a major driver for doctrine revisions when I left, since much of Western naval doctrines were/are based on the idea that you could have a fairly safe and unreachable "seabase" a few hundred nm from shore from which to launch assaults. These kind of very long range area denial weapons upend that thought.