CNN made a pretty big blunder during their coverage of Dolly Parton's death ... showing a pic of an impersonator instead of the real deal ... and now the cable news giant is apologizing.

The embarrassing flub went down Tuesday night ... CNN was airing a montage of Dolly photos, and they mistakenly included an image of Las Vegas impersonator Kelly Vohnn.

The photo hit airwaves during "Laura Coates Live" ... about 12 hours after Dolly's family announced the iconic artist's death ... so it wasn't like CNN was rushing to put together a TV package here.

CNN apologized for the mistake, telling the California Post in a statement ... "We regret the error and apologize to the Parton family."

As for Vohnn, she was shocked by the mix-up. She told the outlet ... "I started getting all these texts in from friends saying that I was on CNN, and I couldn't believe it."

She added that someone at CNN "really messed up," saying ... "I was already heartbroken at losing Dolly because of how much she has given to me as a woman and an artist. But then to see these images of me on screen was just weird."

Vohnn explained she's never tried to pass herself off as the real Dolly ... and found the snafu to be "quite embarrassing."