Blizzard has made a short post this afternoon taking action against what they phrase as "several thousand" Hearthstone accounts found to be botting.

Reddit reports via images that this initial ban is only for three months, after which time botters get their accounts back with all their purchases intact, as the blog explains.

This initial ban may seem rather lenient, and there have certainly been responses to that effect. However, as Blizzard Community Manager Zeriyah clarifies, future bans will not be so lenient:
Originally posted by Blizzard (View Original)Collapse

Accounts discovered to be botting or violating our Terms of Service from here on out will receive a perma-ban.
Zeriyah and Senior Game Designer Ben Brode also posted several tweets on the bans:
@CM_Zeriyah did the botters lose their card collections or anything or was it just the temp ban?
@KindbudiiIchig0 Earnings have not been removed.
@bdbrode @CM_Zeriyah I botted, no excuses. Will I lose my cards? Collecting is important to me. Will I still receive next months card back?
@taeyeon____ss @bdbrode You have not lost your cards, but you won't be able to acquire card backs for the duration of your ban.
@bdbrode Why not reset accounts along with the bans, allowing people to keep portraits and gained gold/cards seems counter to fair-play.
The blog reads as follows:
Originally posted by Blizzard (View Original)Collapse

We've recently banned several thousand Hearthstone accounts that were associated with the use of third-party programs that automate gameplay, otherwise known as “bots” or “botting.” These accounts will be banned until 2015. As we’ve stated, fair play is at the core of the Hearthstone experience, and cheating and botting will not be tolerated.
We’re committed to creating a fun and rewarding environment for our players, and we will continue to closely monitor activities within Hearthstone and take appropriate action against cheating in any form, as outlined in our Terms of Use. From this point on, accounts found to be cheating will be permanently closed without warning.
If you believe that you’ve encountered a possible bot or other form of exploitation, please let us know by emailing our Hacks team at hacks@blizzard.com.
Also from the Reddit thread, here's the image that greets banned players: