Britney Spears' home popped up on the market Monday -- which got her fans thinking she was ready to get the hell outta Cali ... but she isn't going anywhere, TMZ has learned.

Eagle-eyed sleuths probably noticed BS' Thousand Oaks mansion show up on real estate sites as being listed for sale Monday -- and it looked like she was trying to unload it for just under $9 million ... at least based on the public listing.

However, despite the fact this info got published and went wide everywhere -- multiple sources with direct knowledge tell us the whole thing was a hack ... and Britney is NOT packing her bags.

We've learned someone hacked into the Multiple Listing Service -- MLS -- and posted the fake listing.  Other real estate sites, including Realtor.com and Zillow, then picked it up and the fake listing spread like wildfire.

Our sources tell us Brit's management team noticed the listing Monday -- which had some big wig real estate agents attached. We're told Brit's team hit these agents up ... and the agents said they had no involvement whatsoever.

Unclear who hacked the MLS, but in any case ... we're told the powers that be have already yanked it off the service.