The so-called genuine urban artist - real name Anna Georgette Gilford - has been branded "painful".
The family member also claimed that Anna had always lived "in the shadow of her sister".
"To the nation Honey G is funny to watch but to her family it’s embarrassing," the relative told the Daily Star newspaper.
They went on: “She has always lived in the shadow of her sister and finally this is her time to get attention—but it’s painful to watch.
"Anna is a very sensitive soul and to watch her being mocked by the nation is upsetting.”
However an X Factor source insisted: “Honey’s family, including her mum, have been extremely supportive of her.”
Sunday night saw Honey G sail through the latest results show, although some weren't happy about it.
Relley C went home but stuck up for Honey G yesterday, saying: "People don't see what we see and they've not got to know Honey G. They're just seeing what they see on what they see on TV, and if I didn't know Honey and I was watching as a viewer I would probably be like, 'That was a bit of a piss take'.
"But because I know her, I just take my hat off to her at the end of the day, because she's just doing what she's got to do."
The X Factor is back next Saturday and Sunday night on ITV at 8PM.
It's Halloween weekend and there will be a guest performance from reigning winner Louisa Johnson.