Murray was born on 8 September 1959 in Bridge of Allan, Stirlingshire, the daughter of Eileen Shirley and Roy Erskine, an optician and former footballer who had played for Stirling Albion in the 1950s. She says that growing up, there were no indoor tennis courts in Scotland, so she played tennis in the summer and badminton in the winter. She won 64 titles in Scotland during her junior and senior career, and decided to have a go at the professional tour in around 1976. Murray gave up the idea of competing professionally as she was homesick and was robbed in Barcelona. However, she had played against players such as Debbie Jevans and Mariana Simionescu. Murray claims that her playing style did not have any big shots but she was quick around the court and read the game well. She decided to go to the University of Edinburgh to study French and German, before dropping German in favour of business studies. In 1981, she graduated from the University of Edinburgh, and represented Great Britain at the World Student Games. She began coaching and was the initial coach for both her sons before handing over the reins as their professional careers bloomed. In the early 1980s, Murray lived in the West End of Glasgow and was a member of Broomhill Lawn Tennis and Squash club , winning the Club Championships three times and playing for its teams. She remains a visitor to the club. Aside from her own sons, she has coached many players at regional and national level under the auspices of the British tennis governing body, the Lawn Tennis Association. In December 2011 she was elected to lead the British Fed Cup team as their captain. She says she took the job in part to raise the profile of female coaches and alleviate some of the sexism that she says remains in the sport. She resigned as Great Britain's Fed Cup Captain in March 2016. Murray was appointed Officer of the Order of the British Empire in the 2017 Birthday Honours for services to tennis, women in sport, and charity. She is a trustee of the Judy Murray Foundation, a registered charity under Scottish law, with the object of improving access to tennis opportunities across Scotland. In 2020, Murray appeared as a contestant on Celebrity Masterchef
On 7 September 2014 Murray was introduced as a competitor in the 12th series of BBC One's Strictly Come Dancing, paired with professional dancer Anton du Beke. In week eight at Blackpool, however, after dancing a Viennese Waltz to "Let's Go Fly a Kite" from Mary Poppins, the pair had one of the lowest two scores. They were eliminated by a unanimous vote from the judges. Writing in The Daily Telegraph, Michael Hogan tagged his review of the show "Ballroom justice at last as the popular but wooden Mrs Murray leaves Strictly", describing the last dance: "It was Murray’s best yet – not saying much, maybe – scoring her first sevens. She was even more delighted by her four from Craig Revel Horwood." 3 Score from guest judge Donny Osmond.