Arthur Lowe was born in Hayfield, Derbyshire, the only child of Arthur (1888—1971) and his wife Mary Annie (Nan) née Ford (1885—1981). His father worked for a railway company, in charge of shunting theatrical touring companies around Northern England and the Midlands in special trains. Young Arthur went to Chapel Street Junior School in Chapel Street, Levenshulme, Manchester. Lowe’s original intention was to join the Merchant Navy but this idea was thwarted because of his poor eyesight. Working at an aircraft factory he joined the British Army on the eve of World War II, but not before experiencing his first brush with the acting world by working as a stagehand at the Manchester Palace of Varieties. Lowe served in the Middle East with the Duke of Lancaster's Own Yeomanry, and began to take part in shows put on for the troops, which appears to have sparked his desire to act. He left the Army at the end of the war with the rank of Sergeant-Major.

Lowe made his debut at the Hulme Hippodrome repertory theatre, Manchester in 1945, where he was paid £5 per week for twice-nightly performances. He worked with various reps around the country and became known for his character roles including parts in the West End musicals Call Me Madam, Pal Joey and The Pajama Game and eventually featured in at least fifty films. He briefly appeared as a reporter at the end of the Ealing comedy film Kind Hearts and Coronets (1949).

By the 1960s Lowe had successfully made the transition to television and landed a regular role as draper/lay preacher Leonard Swindley in the Northern drama series Coronation Street (1960–65). So popular was his role with viewers that he was eventually given his own spin off series Pardon the Expression (1966) and its sequel Turn out the Lights (1967).

Leonard Swindley was not, however, a role Lowe relished, and he longed to move on to other parts. During the months he was not playing Swindley he was busy on stage or making guest roles in other TV series including Z-Cars and The Avengers. He also had prominent parts in the Lindsay Anderson films This Sporting Life (1963), if.... (1968) and multiple roles in O Lucky Man! (1973).

In 1968 Lowe was invited by Sir Laurence Olivier to act at the National Theatre at the Old Vic and appeared in Somerset Maugham's Home and Beauty in 1968 and later The Tempest in 1974 with John Gielgud.

Lowe married Joan Cooper on 10 January 1948. They had met in 1945 when she was his leading lady at Hulme Hippodrome and they remained together until his death. Their son Stephen Lowe was born in January 1953.

In 1968, Lowe was cast in his most famous role, Captain George Mainwaring in the BBC sitcom Dad's Army. It has often been remarked by his former colleagues that this was the role Lowe played which most resembled himself: pompous and bumbling, although he also successfully played Mainwaring's drunken brother Barry Mainwaring in the 1975 Christmas episode "My Brother and I". He went on to take the character into a radio series, a stage play and a feature length film.

When not involved in Dad's Army Lowe was kept busy with appearances in plays at the National Theatre and the Royal Court Theatre. He continued to appear in films, including Spike Milligan's surreal The Bed Sitting Room, in which he mutates into a parrot, as a drunken butler in The Ruling Class with Peter O'Toole (for which he received great personal acclaim) and a jokey Vincent Price horror movie Theatre of Blood as one of the unfortunate critics.

On television he appeared as a guest performer on The Morecambe and Wise Show, alongside Richard Briers in a series of Ben Travers farces for the BBC, as the pompous Dr Maxwell in the ITV comedy Doctor at Large and Redvers Bodkin, a snooty, old-fashioned butler in the short-lived sitcom The Last of the Baskets (1971–72).

Between 1971 and 1973 Lowe joined Dad's Army colleague Ian Lavender on the BBC radio comedy Parsley Sidings. In 1974 he played Mr Micawber in the BBC serial David Copperfield. He employed a multitude of voices on the 1975 BBC animated television series Mr. Men, where he voiced all the characters as well as narrated.