Catherine Gowing, 37, was last seen alive on Friday evening, leaving the practice where she worked in Mold, North Wales.
Officers were alerted when she failed to turn up for work on Monday morning, having also missed an appointment over the weekend.
The following day they arrested a 46-year-old local man on suspicion of her murder and launched a major inquiry into the vet’s disappearance.
Miss Gowing’s sister, Emma, said her family were devastated by the disappearance.
‘She is the light of our family and we can’t imagine that light gone,’ she added.
Miss Gowing’s elderly parents, John and Maureen, who are both in their 80s, were being comforted by friends and relatives at the family farm in Clonlee Clareen, Birr, Offaly.
Her uncle, Edward Gowing, also a vet, said the family had been told by police that there was little chance of Miss Gowing being found safe and well.
He added: ‘To say we are in shock is an understatement.
‘We have been told that it is a murder investigation. Catherine was a very bubbly, outgoing person.
'She was a great social mixer and had lots of friends.’
He said his niece was passionate about her career as a vet and was very academic.
But Mr Gowing said it was her intention was to return to Ireland and take over the family farm.
Investigation: Police teams search the home of missing vet Catherine Gowing in New Brighton near Mold, north Wales
Sensitive operation: Forensic officers in white overalls arrive at Miss Gowing's home to take photographs and search for cluesHer uncle added: ‘She is two years working as a vet. She loved it and loved living in Wales. But her real passion was farming.
‘She was going to come back here at Christmas and most likely take over the family farm. She loved nature and farming. She was a very independent minded woman. Everyone speaks highly of her.’
Horse breeder Jean Walker said: ‘Catherine was a lovely person who came out to see to one of my ponies. She was very professional.’
Inquiry: A forensic expert in white overalls consults a community support officer at Miss Gowing's home near Mold, North WalesMiss Gowing is the youngest of two girls in the family. Her elder sister, Emma, and brother-in-law, Shay, travelled to Wales yesterday to help police with their inquiry.
Mr Gowing said officers were alerted on Monday when Miss Gowing failed to turn up at work. They discovered her Irish registered car was missing, but a 4x4 she used for work was on the drive with the keys inside and her house was open.
It is understood flatmate Miss Doyle, who is from Robinstown, in Meath, was away in Ireland for the weekend.
Mr Gowing said the family have been told that the man in custody was known to his niece and may have had access to the house - although he was not in a relationship with the single vet.
Miss Gowing, originally from Birr, County Offaly, in the Republic of Ireland, lived with her flatmate and fellow Irish vet, Jane Doyle, 37, in a modern semi-detached house in New Brighton, near Mold.
The £150,000 property, in a quiet cul-de-sac, is owned by the DE Evans Veterinary Surgery, where both women worked.
Yesterday the house was sealed off by police and scenes of crime officers were scouring the inside for clues.
Officers have appealed for information on the location of Miss Gowing’s burgundy Renault Clio, which has Irish plates, and has also been missing since last week.
Detective Superintendent John Hanson, of North Wales police, said he feared Miss Gowing may have come to ‘some significant harm.’
Standing guard: Community support officers keep watch outside Miss Gowing's home as the investigation into her disappearance continues
Murder probe: North Wales police officers fear Miss Gowing may have come to 'some significant harm'‘We are increasingly concerned about Catherine’s welfare and have no knowledge as to her current whereabouts,’ he said.
‘This is totally out of character for Catherine who maintains regular contact with her family, friends and work colleagues and I fear she may have come to some significant harm.’
Det Supt Hanson said the man arrested was known to Miss Gowing, but refused to elaborate any more on whether they were in a relationship, friends or mere acquaintances.
Neighbours described Miss Gowing as a ‘lovely girl’.
Search: Police are trying to trace Miss Gowing's Renault Clio, bearing an Irish registration plate, which is also missing from her homeMichelle Shaw, who lives nearby, said she last saw Miss Gowing when she went to work on Friday morning.
‘Catherine looked after my horses and was always a very pleasant woman,’ she said.
‘She was really nice and would always help anyone.
‘I used to have a bit of a joke and laugh with her, it’s just so sad.
‘It’s such a shock because it’s so quiet round here and she’s such a pleasant, open and happy woman.’
Sighting: Miss Gowing was last seen leaving the veterinary practice where she worked in MoldMrs Shaw said the two women rarely had any visitors.
‘I never saw a boyfriend or anything like that,’ she added.
‘On Friday night my daughter noticed that the Renault Clio which has been reported missing wasn’t on her drive.
‘That was strange because she only ever used her work car unless she was going on holiday.
‘I’m praying and hoping the police find her and she’s safe.
‘People of her age don’t just disappear, and why anyone would want to hurt her is beyond me.’
Another neighbour, Elizabeth Purcell, said Miss Gowing was a ‘quiet and friendly woman.’
‘She was a very quiet girl, very nice,’ Mrs Purcell said. ‘She was absolutely lovely with my dog and we’re just very, very upset.’
Photographer Hadyn Iball, a long-term customer of Miss Gowing’s surgery, described her as ‘compassionate’ and ‘personable.’
‘We always found her to be an excellent vet, very thorough and extremely personable,’ he said. ‘We are very sad to hear this news and our thoughts and sympathies go out to her family at this time.’
No-one from the veterinary surgery would comment on Miss Gowing’s disappearance.
Anyone with information about the whereabouts of Miss Gowing’s burgundy coloured Renault Clio, which has an Irish registration plate 00D99970, should contact North Wales police on 101 or Crimestoppers on (0800) 555111.