Manmohan Singh was born in Gag, now in Pakistan, on September 26, 1932.
Kher, who essays Singh in the film, took to Twitter to share his thoughts, saying his portrayal is "full of sincerity and honesty".
"Respected #DrManmohanSingh! Here is wishing you a very happy and healthy birthday. Maybe I will get an opportunity to have a cup of tea and a piece of cake with you if you ever watch our film.
"I promise, you will like my portrayal. It is full of sincerity and honesty. Regards," the actor wrote.
The film is based on the book of the same name, written by Sanjay Baru, who served as the media advisor of Manmohan Singh from 2004 to 2008.
It is being made in English and Hindi by debutante Vijay Ratnakar Gutte and it produced by Bohra Brothers.