Melik-Parsadanova (nee Fonberstein) was born in Leningrad (St. Petersburg) in 1925. Her father, a Jewish violinist and an old bolshevik (who joined the Bolshevik party before the revolution of 1917), was subjected to repression and exiled to Kazakhstan in 1934. The girl then moved to Tbilisi with her mother, a Georgian economist, who was shortly after also arrested but subsequently released. In 1938 they moved to Baku, Azerbaijan, where Maya would study at the Architecture-Construction Department of Azerbaijan Industrial Institute in 1943-1949. She married her fellow-student Viktor Melik-Parsadanov, who came from an Armenian family. 

Upon graduating, the couple moved to Sevastopol, Crimea, where they worked on the reconstruction of the city in the aftermath of the Second World War. In 1962, Melik-Parsadanov was appointed the head of Crimea Regional Department of Construction and Architecture, and the family moved to Simferopol, the capital of Crimea region, where Melik-Parsadanova worked at KrymNIIproekt (Scientific-Research Institute of Design, Crimea) until her retirement. Despite being overshadowed by her more professionally successful husband, with whom she had two daughters, Melik-Parsadanova was a prolific architect, who occupied several leading positions: chief workshop architect, chief architect of the institute’s Simferopol department, and the chief architect of the departments of typified and experimental design.        

Among her works are residential buildings and the House of Culture of  Construction Workers in Sevastopol, microdistricts and residential buildings in Simferopol, Donetsk, Novorossiysk and other cities in Ukraine and southern Russia, department stores in Simferopol and Alushta, sanatoriums in Alushta.

Melik-Parsadanova was awarded the title of Honorary Architect of the Autonomous Republic of Crimea in 2000.