Update: PUBG's official Twitter account has stated that an error causing random players to be banned from the game has been fixed, and that any accounts banned mistakenly have been reinstated. However, players are claiming they're still locked out of the game, so perhaps the fix will take a while to feed through.
It looks like the initial problem lasted about six hours or so—it was caused by an update to the game's anti-cheat service earlier today.
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PC players, the detection logic related bug that occurred after today's anti-cheat update has been fixed and all the temp bans caused by it were lifted. Thank you for your patience.March 8, 2018
PlayerUnknown's Battlegrounds' hacker problem is well documented, and developer Bluehole is constantly pushing updates to the game's anti-cheat system in order to catch the worst offenders. Unfortunately, the latest update has resulted in some friendly fire, with scores of players claiming they've been banned without ever having cheated. The developer has confirmed that the update is "temporarily preventing some players from accessing our game".
PC players, we are aware of a detection logic related bug that occurred after today's anti-cheat update and is temporarily preventing some players from accessing our game. Please accept our apologies. We are working on a fix as fast as we can.March 8, 2018
Numerous Twitter users on this thread uploaded screenshots of a ban message, which said they were banned because of "abnormal game logs" and "too many suspected complaints for using illegal software".
Some players in this Reddit thread who were initially banned are now able to play again, so if it's happened to you, I'd try again in a few hours. I imagine it'd be really frustrating getting banned for cheating when you've done nothing wrong, especially when you see other players in the game blatantly hacking, zooming around the map at five times their normal speed (which is one I've come across), or auto-headshotting people.
To give an idea of the scale of the problem, the game banned more than one million players in January, including 100,000 in a single wave. It's truly a mammoth task—last month, the official account of the game's anti-cheat service said that despite the bans "things continue to escalate".