The 62-year-old dance teacher had shared some of the abusive messages she received online over the weekend after saying she would have wanted to save The One Show's Richie Anderson, 34, over former X Factor star Fleur East, 34, but was outvoted by the other judges.
Ballas has now tweeted: "I have received many apologies over the weekend regarding hurtful messages I’ve received on social media. All apologies are accepted and from now on let’s all respect each other and enjoy the show. Love to you all."
The Strictly judge shared some of the insults she had been sent on social media after her critiques of the celebrity dancers aired in Movies Week.
One message called her a "c***" while another said she was an "unpleasant, sour-faced old dear".
She said: "This is the language and messages I get along with other disgusting low life messages. Because they think they are multiple British open to the world champions and qualified to judge. Very sad indeed."
Ballas won the Professional Latin title at the Blackpool Dance Festival three times during her professional career.
In week three of Strictly, the judges were surprised when the public vote landed Anderson and East in the dance-off, as they had both achieved reasonable scores for their performances.
After the couples danced again Motsi Mabuse, Craig Revel Horwood and Anton Du Beke all chose to save East and her partner Vito Coppola.
Ballas - who as head judge would have the casting vote in the event of a tie - said she had wanted to save Anderson and Giovanni Pernice.
Watch: Who Is Strictly's Richie Anderson?
This led to some viewers accusing Ballas of being "sexist" claiming she favours male contestants over female.
One said: "Shirley Ballas should be removed from the panel, she’s setting a bad example, she cannot celebrate the young, female celebrities. Her views are outdated and sexist. Please let this be her last year, or preferably week on, #Strictly"
Another tweeted: "Sexist Shirley would have saved Richie over Fleur. Ffs, Richie’s dance had negligible samba content and he fannied around the judges’ tables for half the dance. Fleur’s dance was elegant and beautiful. She has no credibility as a judge #Strictly"
And another viewer commented: "The way Shirley speaks to the women is unacceptable. She clearly has an issue with young attractive women and this affects her judge. Furthermore, the suggestive tone she uses to the male celebrities is sexist. All been happening since she began."
In 2019 she voted for comedian Chris Ramsey, 36, over footballer Alex Scott in a dance off.
And that same year she eliminated former Coronation Street star Catherine Tyldesley, 39 to save BBC Breakfast presenter Mike Bushell, 56.
This year Ballas has showed some favouritism towards the male contestants.
She told Kiss Radio DJ Tyler West, 26: “You’re the real deal. You bring something you can’t teach."
Ballas also said that actor Will Mellor, 46, was “easy on the eye”.
And in 2019 she said 38-year-old Emmerdale actor Kelvin Fletcher, who went on to win the show: “Sent my temperature through the roof.”