Myer was born in Krychaw (Krichev), Mogilev Governorate, Russian Empire (within the Pale of Settlement;, present-day Belarus), the youngest of eleven children born to Ezekiel Baevski, a Hebrew scholar, and his wife, Koona Dubrusha (née Shur). He was educated at the Jewish Elementary School in Krichev, and later managed his mother's drapery Business. He emigrated to Melbourne in August 1899 with very little money and little knowledge of English to join his elder brother, Elcon Myer (1875–1938), who had left Russia two years earlier.

On 8 March 1905, Myer married Hannah Nance Flegeltaub (1868–1963), a cousin of Travers Vale. They had no children, but in 1911 he acted as guardian of his nephew, Norman Myer. In mid-1919, Sidney Myer went to the United States to study Retailing. While there he divorced Hannah in Reno, Nevada, although the divorce was not recognised under Australian law.

In 1911 he purchased the Business of Wright and Neil, Drapers, in Bourke Street, near the General Post Office, and a new building was completed and opened in 1914. The Doveton woollen mills at Ballarat were purchased in 1918, and in 1921 a new building fronting on Post Office Place, was added at Melbourne. These became the Myer chain of department stores. The Myer Emporium grew with the purchase of such old established businesses as Robertson & Moffat, and Stephens & Sons.

In 1920, he converted to Anglicanism when he married his second wife. On 8 January 1920, he married (Margery) Merlyn Baillieu (later Dame Merlyn Myer), on her 20th birthday. They had two daughters and two sons: Kenneth AC (1 March 1921 – 30 July 1992), Neilma (7 November 1922 – 15 June 2015, later Neilma Gantner), Sidney Baillieu Myer AC (born 11 January 1926), and Marigold Merlyn Baillieu Myer (Lady Southey AC) (born 2 May 1928). Merlyn traveled to San Francisco, California for the birth of each of their four children to ensure they would be considered legitimate.

A Violinist who enjoyed music, Sidney Myer established free, open-air concerts with the Melbourne Symphony Orchestra in 1929, which were always well attended by Melburnians.

During the Depression of the 1930s, Myer felt a responsibility to contribute something to the community that had assisted him in achieving Business success and a personal fortune. Rather than terminate employment of workers in his Department Store, all staff, including himself, had their wages cut. Relief work was personally financed by a £22,000 sum, to provide employment opportunities. For the unemployed at Christmas, he financed a Christmas dinner for 10,000 people at the Royal Exhibition Building, including a gift for every child.

In 1925, Myer Ltd was listed on the Melbourne Stock Exchange and the new building on the Lonsdale Street frontage was begun. A separate building in Queensberry Street, Melbourne, was put up in 1928, and the Collins Street businesses of T. Webb and Sons, china importers, and W. H. Rocke and Company, house furnishers, were bought and transferred to the Bourke-street building. A public company had in the meantime been formed which by 1934 had a paid-up capital of nearly £2,500,000. A controlling interest in Marshall's Limited of Adelaide was also acquired. The company was then employing 5,300 people with medical and nursing aid for the staff, and rest homes for them at the seaside and in the Dandenong Ranges. Some of Myer's friends and Business associates feared the Business was developing too rapidly but it was in a prosperous state and fast recovering from the effects of the Depression, when Myer died suddenly on 5 September 1934, at age 56.

The Myers returned to Australia in 1929. Ken Myer was a philanthropist, a prime mover behind the Victorian Arts Centre; chairman of the Australian Broadcasting Corporation; and was offered and declined the governor-generalship of Australia. Ken Myer and his brother Baillieu set up the Myer Foundation in 1959. Sidney Baillieu Myer married Sarah June Hordern (born 1935) of the Sydney Hordern Retailing family on 15 December 1955, thus linking two of Australia's wealthiest families. Sidney Baillieu Myer and Sarah Hordern had three children: Sid Myer, Rupert Myer and Samantha Myer.

Myer's will was proved at £922,000. His funeral was attended by some 100,000 people. One-tenth of his estate went to establish the Sidney Myer Charitable Trust, now known as the Sidney Myer Fund, to continue the tradition of philanthropy begun by its founder. The most famous philanthropic funding was for the construction of the Sidney Myer Music Bowl in the Kings Domain, Melbourne in 1958, which is named in his honour.

Sidney Myer's gravesite, a sepulchre for the reception of urns of ashes, is in Box Hill Public Cemetery in Melbourne. Also interred in the tomb are Dame Merlyn Myer, and Ken Myer and his wife, Yasuko, who perished together in a light aircraft crash in Alaska in 1992. The grave is listed on the Victorian Heritage Register.