Sandrich was born in New York City, to a Jewish family. He was an engineering student at Columbia University when he began in the film business by accident. While visiting a friend on a film set, he saw that the director had a problem in setting up a shot; Sandrich offered his advice. It worked. He then entered into the movies in the prop department, and became a director specializing in several comedy shorts in 1927. He then made his first feature the next year, but returned to shorts after sound arrival. In 1933, he directed the Academy Award-winning short, So This Is Harris!. He later returned to feature films, most notably comedies, starring the team of Bert Wheeler and Robert Woolsey in Hips, Hips, Hooray!. In 1934, Sandrich soon gained his first directorial assignment with the Fred Astaire-Ginger Rogers musical The Gay Divorcee, which proved a success.
In 1945, while in pre-production on a follow-up to Holiday Inn called Blue Skies, starring Bing Crosby and featuring Irving Berlin's music, and serving as president of the Directors Guild, Sandrich died suddenly, of heart failure. He was at that time one of the most trusted and influential directors in Hollywood, respected by his colleagues and the studio management. His interment was at Home of Peace Cemetery.