"Big Brother" contestant Shelly Moore pissed off America when she voted to evict fan favorite Jeff Schroeder last week -- and now TMZ has learned her family has been receiving death threats from deranged fans because of the move.

Sources close to Shelly tell us ... the reality star's family has received multiple phone calls from people threatening violence ... even making threats against Shelly's 8-year-old daughter.

We're told Shelly's employer has also been receiving harassing phone calls -- demanding the company fire Shelly immediately because of the way she voted on the show.

Sources tell us Shelly's family is preparing to get the FBI involved -- because they're taking the threats VERY seriously.