The actor's agent confirmed that of Louella Michie, 25, was the woman who was killed at the Dorset music festival today.
A 28-year-old man from London has been arrested on suspicion of her murder.
Police said her body was found in a wooded area of the festival site in Lulworth, Dorset.
Louella was the youngest daughter of Mr Michie, who also appeared in Casualty and Taggart, and his wife Carol Fletcher, who was previously a dancer for television troupe Hot Gossip.
In a statement, his agent said: 'Sadly, I can confirm the tragic death of John Michie's daughter, Louella, at Bestival.
'John and his wife Carol ask that the privacy of their family be respected at this traumatic time.'
Det Chief Inspector Sarah Derbyshire said: "Following the discovery of the woman's body we have now launched an investigation into her death. We have specially trained officers supporting her family at this very difficult time.
"We are working closely with the festival organisers and I would appeal to anyone with any information about the incident to contact Dorset Police."
In a statement, organizers of Bestival said: "Following today's news announcement, the team at Bestival are devastated to hear about this tragic news.
"We continue to support the police in their ongoing investigation and our thoughts and prayers are with all the woman's family and friends."
Michie is best known as playing Rover Return landlord Karl Munro where he had the distinction of burning down the street's favourite pub in one of the soap's most gripping storylines.
He also starred in Taggart playing DI Robbie Ross for 12 years. Michie is currently playing neurosurgeon Guy Self in BBC's medical drama Holby City.
The 60-year-old has two other children, Daisy, 27, a stylist, and Sam, 26, a music video director.
Arsenal football fan Louella, the youngest of his three children, worked as a dancer and also lived in North London.
Officers were called to the site just before 1am on Monday to reports revellers were concerned for the welfare of the 25-year-old woman
Dorset Police said the arrest was 'to enable officers to conduct an interview under caution to help establish the full circumstances'.
Some 30,000 revellers descended on the site for the four-day event but forensic officers were working at the scene as the festival came to a close and a cordon remains in place.
A spokesman for the event said the matter was currently being dealt with by Dorset Police.
Bestival Police last week issued a warning about a rogue batch of tablets found on the festival site.
Officers tweeted a photo of a tablet and urged festival goers to dispose of them as they contained 'unknown chemicals'.
Drugs have not been linked to the death of the 25-year-old woman.
Detective Chief Inspector Sarah Derbyshire said: 'Following the discovery of the woman's body we have now launched an investigation into her death.
'We have specially-trained officers supporting her family at this very difficult time.
'Inquiries are now under way to establish how she died.
'A post-mortem examination will be carried out in due course and this should give us more of an indication as to the cause of her death.
'We are working closely with the festival organisers and I would appeal to anyone with any information about the incident to contact Dorset Police.'
A force spokesman said the woman's family had been informed and the coroner had been notified of her death.
Anyone with information is asked to contact the force at www.dorset.police.uk, via email 101@dorset.pnn.police.uk or by calling 101, quoting incident number 11:36.
In a statement, Bestival said: 'Following today's news announcement, the team at Bestival are devastated to hear about this tragic news.
'We continue to support the police in their ongoing investigation and our thoughts and prayers are with all the woman's family and friends.'
Last year, organisers announced Bestival would be moved from the Isle of Wight, where it was previously held, to the Dorset site.
The line-up this year included The XX, Dizzee Rascal, Rag'n'Bone Man, Pet Shop Boys, Wiley and Laura Mvula.
On Sunday, festival organisers were forced to close the main arena, the Castle Stage and Ambient Forest due to high winds.
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