McMurray was born in Port Melbourne, Victoria in 1889.
Jack showed a keen interest in football. He began umpiring in the South Suburban competition aged 16, but the next year decided that he wanted to play, so joined the Rosedale juniors at Port Melbourne.
He found the going tough by virtue of his very slight physique (155 cm and 50 kg) and in 1908 he returned to umpiring and officiated in the Metropolitan Junior Association.
Three years later, his progression found him umpiring in the Victorian Junior Association and in 1913 he was appointed to the Victorian Football Association (VFA). In 1914 he handled the First Semi-Final and two weeks later the Grand Final between North Melbourne and Footscray. In 1915 he umpired through the home and away season but could not dislodge Tom Kendall who umpired all three finals matches that year.
In June 1920 he umpired the rest of the season in the seniors and becoming a first choice umpire. His first significant matches were the 1921 finals series, where he umpired three of the four finals, Jack Elder being appointed to the Second Semi-Final.
McMurray now established himself as 'the' umpire of the period, having almost a monopoly on finals, interstate and carnival matches. He was in charge of the first half of the only match ever between the VFL and VFA Premiers. Played in 1924, after a particularly unsuccessful League final series experiment, Footscray defeated Essendon and McMurray shared duties with the VFA's representative James Leheny.
In 1929 the Great Depression led McMurray to accept an offer from the Northern Tasmanian Football Association (NTFA). He was appointed to umpire for £15 a week (at the time the highest fee ever paid).
He returned to Melbourne at the end of the season and was immediately reappointed to the VFL for 1930.
One famous incident in McMurray's career involved the great Haydn Bunton Sr. In 1934, Bunton dominated the last game of the season and as he walked off the ground he made a flippant remark to McMurray, along the lines of: "That wasn't bad today, Jack."
In August 1936, 20 seasons after his first VFL match, McMurray became the first umpire to officiate in 300 VFL matches. He eventually retired from VFL umpiring at the end of that season having umpired a total of 307 matches (including 4 as a boundary umpire), 23 finals (including 5 Grand Finals) and a record 15 Interstate appointments.
He umpired one final season in the country leagues and at the end of 1937, aged 47, left the field for good.
He was made a life-member of the League in 1980 matching his 1933 Life Membership of the VFL Umpires Association. McMurray was further recognised by the awarding of the Jack McMurray Scholarships. These were presented to the best two first year umpires on the Cadet Squad list each year between and 1987 and 1991 by the then VFL Commission.
McMurray was inducted to the Australian Football Hall of Fame in 1996.
His son Jack McMurray Jr. was also a highly respected umpire, inducted into the Hall of Fame.