IBNS: RRR was also nominated for Best Director, Best Picture, and Best Visual Effects.
The twin awards come days after Naatu Naatu won the best song in the Golden Globe Awards.
RRR has been shortlisted for the 95th Academy Awards or Oscars in various categories.
The film that had earned Rs. 1,200 crores globally was released on Mar 25, 2022.
Jr NTR and Ram Charan have played the freedom fighters in the period drama, which is set in British India.
Apart from the two south Indian superstars, the film features Hindi film veteran Ajay Devgn and leading Bollywood actor Alia Bhatt in the lead.
Naatu Naatu was composed by music director MM Keeravaani and sung by Kala Bhairava and Rahul Sipligunj.