Shailendra, who died on 14 December 1966, aged 43, was known for his association with filmmaker Raj Kapoor and music composers Shankar-Jaikishan.
The news was announced by chairperson of local municipality, Manisha Gupta, at a function in Shailendra's memory, titled "Jeena isi ka naam hai", at the Birla Institute of Management and Technology in Greater Noida.
Shailendra's son, Dinesh, said he was extremely happy with the honour for his late father.
"I never thought people of Mathura would be so happy to know that he spent 16 years of life growing up here."
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Shailendra wrote lyrics for several successful Hindi film songs in the 1950s and the 1960s.
He is best known for songs like "Awara Hoon", "Ramaiya Vastavaiya", "Mud Mud Ke Na Dekh", "Mera Joota Hai Japani", "Aaj Phir Jeene Ki", "Gata Rahe Mera Dil", "Ajeeb Dastan Hai Yeh" among others.
Shailendra shared a rapport with composers such as Salil Chowdhary ("Madhumati"), Sachin Dev Burman ("Guide", "Bandini", "Kala Bazar"), and Ravi Shankar ("Anuradha").
He also gave hits working with filmmakers like Bimal Roy ("Do Bigha Zameen", "Madhumati", "Bandini") and Vijay Anand ("Guide" and "Kala Bazar").