Ms Holdsworth suffered serious head and back injuries on Friday in a collision in Hartlepool in north-east England.
The 36-year-old, who was club physio for Watsonians, died the next day in hospital. Police last night named her as the driver of a car involved in the crash.
Her sister, Fiona Chadwick, described her as a “beloved sister who will be greatly missed” and said her family and friends have been left devastated.
Paul McGinley, head of performance medical at Scottish Rugby Union, said: “Keri worked to provide care to Scottish Rugby players over a number of years, and was an outstanding professional and person.
“Some of our team members knew her as a player, others as a colleague and friend who worked with our Scotland women’s under-20 squad.
“She was a fantastically upbeat and positive person who will be very sorely missed, but very fondly remembered.”
Ms Holdsworth suffered serious injuries in the crash between her Renault Clio and a BMW on the A19, police said. She was taken to the James Cook University Hospital in Middlesbrough but died on Saturday.
Ms Holdsworth, a former back-row forward, won 15 caps for her country with a number of age-grade squads.
While with Watsonians, she made her debut for Scotland Women against Ireland in 2008, continuing in to the 6 Nations and that year’s FIRA tournament. She played in seven of Scotland Women’s nine internationals between January and May 2009 and into the 2010 Women’s Rugby World Cup, making her last appearance in the blue jersey against Canada.
Scotland Women head coach Jules Maxton said: “Keri’s experience as an internationalist herself made her particularly intuitive to the needs of our players.
“Her understanding, caring and patience were massively appreciated by all the players and coaches who she worked with over the years.”
Scottish Rugby Council member Dee Bradbury, said: “It’s tragic news and our thoughts are with her friends and family at this time. Keri will be very sorely missed by the Scottish rugby family.”
Born in Broxburn, Ms Holdsworth worked as a senior physiotherapist at Edinburgh University’s Fitness Assessment and Sports Injuries Centre.
Ms Holdsworth gained a physiotherapy degree from Edinburgh’s Queen Margaret University and a BSC in maths, sport and exercise science at the University of Birmingham.