Mukherjee was born in Dhakuria, Calcutta, on 4 October 1931 to Narendranath Mukherjee, a railway official, and Hemprova Devi. She was the youngest of six children. Her grandfather was a police officer, and the family had lived in Dhakuria since 1911. Sandhya started her music training under the direction of Pandit Santosh Kumar Basu, Professor A T Kannan, and Professor Chinmoy Lahiri. However, her guru was Ustad Bade Ghulam Ali Khan followed by his son Ustad Munavvar Ali Khan, under whom she mastered Indian classical music. According to Manorma Sharma, "Sandhya has been able to maintain her popularity as a classical vocalist even after acquiring the gloss and the glow of playback singing.
Though classically trained, the bulk of her work consists of Bengali modern songs. She began her career in Mumbai singing Hindi songs, starting with a song in the film Taarana in 1950. She sang, as a playback singer, in 17 Hindi films. She decided to come back to and settle in her home city Kolkata in 1952 due to personal reasons. She married Bengali poet Shymal Gupta in 1966. Gupta went on to write the lyrics for many of her songs. She received Banga Bhushan the highest civilian honor in the Indian state of West Bengal in 2011. She also won the National film award for best playback singer for her songs in the films Jay Jayanti and Nishi Padma in the year 1970.
Her best-known collaboration is arguable with the Bengali singer Hemanta Mukherjee with whom she sang numerous duets, primarily as playback for Bengali films. Hemanta and Sandhya became known as the voices behind the pairings of the Bengali superstar Uttam Kumar and his numerous heroines, most notably being the actress Suchitra Sen, whose singing voice she became. Besides Hemanta's Mukherjee compositions, her largest body of work is with Robin Chattopadhyay and Nachiketa Ghosh.
During the Bangladesh Liberation War, she joined the mass movement among Indian Bengali artists to raise money for the millions of refugees who had poured into Kolkata and West Bengal to escape the fighting, and to raise global awareness for the cause of Bangladesh. She assisted Bangladeshi musician Samar as he set up the Swadhin Bangla Betar Kendra, the clandestine radio station broadcasting to Bangladesh, and recorded several patriotic songs for him. On the occasion of the release of Sheikh Mujib Rahman the imprisoned leader of the new country of Bangladesh, she released a song Bangabandhu Tumi Phirey Ele. She later became one of the first foreign artists to visit Dhaka, performing at an open-air concert in Paltan Maidan in Dhaka to celebrate the first Ekushey February after Bangladeshi independence in 1971.
On 26 January 2022, on Republic day and a few days before testing positive for Covid 19, Mukherjee was awarded the Padma Shri for her performance in music. However, she refused the award, labeling it "disparaging and degrading". Mukherjee died of cardiac arrest at a private hospital in Kolkata on 15 February 2022, at the age of 90.