Thakur was born in a Bengali musical family in Kolkata. Her father Shakti Thakur is a Bengali singer and her sister Mehuli Thakur is also a playback singer. She was trained in Hindustani classical music under Pandit Jagdish Prasad and Pandit Ajoy Chakraborty. She has learnt hip-hop and Bharatanatyam and is also a trained Salsa dancer.

Thakur started singing in school and college competitions and performing at local functions, and received the Best Playback Singer award at the Anandalok Awards for the serial Sri Ramkrishna when she was 14. She rose to popularity after placing ninth in Indian Idol 2.

She had to struggle even after Indian Idol to get a strong foothold in the music industry. She got an offer from music director Pritam Chakraborty to sing two songs for the Bollywood film Race in 2008 – "Khwab Dekhe (Sexy Lady)" and "Zara Zara Touch Me". She was originally scheduled to sing only one song, but her first recording impressed the film's directors Abbas–Mustan enough for them to book her a second. "Zara Zara Touch Me" was enormously successful, becoming the fourth-most-played song on Indian radio during the first half of 2008. She also got nominated for an IIFA Award for Best Female Playback and an Apsara Award for Best Female Playback Singer for the song "Zara Zara Touch Me". Monali's first large format live concert was at Powai Sarvajanin Durgotsav in 2011.

She was a judge in the Bengali music reality show Bengali Sa Re Ga Ma Pa Li'l Champs for two years. She also appeared in the Bengali show Key Hobe Biggest Fan and was part of Coke Studio. She briefly dated Meiyang Chang.^[12][13]

In 2014,Thakur won the Filmfare Award for Best Female Playback Singer for the song "Sawaar Loon" from the film Lootera.^[14] In March 2016, she received the National Film Award for Best Female Playback Singer for the song "Moh Moh Ke Dhaage" from the film Dum Laga Ke Haisha^[15] and earned a nomination at the Filmfare Award for Best Female Playback Singer for the same.^[16]

As a child, she appeared in a Bengali television soap, Aalokito ek Indu, in which she played the lead role Indubala.^[17] It was followed by two telefilms,^[17] including Sudeshna Roy's Phagune Agun in which she was seen as Ruman.^[5] She made her acting debut in Raja Sen's Bengali film Krishnakanter Will,^[18] in which she played the role of Bhromor.^[19] In 2014, she made her Bollywood debut in Nagesh Kukunoor's Lakshmi.^[20] The film is about human trafficking and child prostitution and Thakur plays a 15-year-old girl who gets trapped in it.^[21] She will be seen in Abbas Tyrewala's multistarrer Mango.^[22] She also acted in a short film titled Jangle Bells along with Namit Das. The film came out in Christmas of 2015.^[23]