Carrie Ann Inaba took Val Chmerkovskiy‘s Will Smithjoke as more than just a punchline … telling show officials she felt threatened by the ‘DWTS’ pro … TMZ has learned.

Sources familiar with the situation tell TMZ … Carrie Ann was so heated over Val’s remarks, she raised the issue with BBC Productions’ HR department, demanding something be done.

Another source tells TMZ BBC, who produces DWTS, launched the investigation after seeing the joke. The source would not confirm whether Carrie complained.

We’re told Val was informed the production company had to follow its guidelines and protocols … and he was subsequently suspended for one episode.

As TMZ previously reported, the dramaerupted after Carrie Ann criticized Val’s wife, Jenna Johnson, for including a lift during her routine with Harry Shum Jr.

Val fired back on social media, joking viewers almost saw the “Fresh Prince” enter the ballroom … a reference to Smith slappingChris Rock at the Oscars.

Val later apologized to Carrie Ann … but that didn’t stop BBC from benching him, with Alan Bersten stepping in to dance with Val’s partner, Jenna Dewan.

We’re also told he’s received plenty of support from his colleagues, and rumors that he unfollowed Carrie Ann, Alan and Emma Slater are bogus. Sources say he never followed them in the first place.