Born in 1893 to Lithuanian emigrants Louis E. and Cecelia Fineberg Meltzer in 1893, Arthur Meltzer learned the skills he would use as an adult to craft frames and furniture at an early age. He apprenticed as a young man at the Ford and McNutt Stained Glass Company, where he stayed for six years, until he enlisted in the Army to serve in World War I.

After his two-year service in the Army, Meltzer traveled to Philadelphia, where he had an uncle, and in 1919 he enrolled at the Pennsylvania Academy of the Fine Arts. He studied under Daniel Garber, Joseph T. Pearson, Jr., Hugh Breckenridge, Robert Vennoh and Arthur B. Carles. He was awarded the prestigious William E. Cresson Traveling Scholarship, and he traveled to Europe, where he painted and visited many museums throughout the continent.

He met his future wife, Paulette Van Roekens, at the Philadelphia School of Design for Women (now Moore School of Art and Design), where he joined the faculty in 1924 and became the head of the Fine Arts Department. They married in 1927 and settled in Trevose, Pennsylvania, where they lived together for over sixty years.

Meltzer exhibited frequently at PAFA and won their Fellowship Prize in 1925. His work was exhibited, and won numerous prizes at institutions throughout the country, including the Philadelphia Sketch Club; the National Academy of Design; the Corcoran Gallery in Washington, DC; the Woodmere Art Gallery (now the Woodmere Art Museum); and the Phillips Mill Art Association in New Hope.

His paintings vary in subject matter, ranging from painting to life drawing, to anatomy and portraiture. His painterly style reveals itself in his many still lifes as well as in his beautifully rendered landscapes of Bucks and Berks Counties and Mystic, Connecticut. Meltzer died at the age of ninety-five at Abington Memorial Hospital.