Modi took to Twitter to wish Parrikar and appreciated the chief minister's "hardworking nature" and commitment towards development of the coastal state.
"Birthday greetings to my friend and Goa's CM @manoharparrikarji. Parrikarji is known for his compassionate, down to earth and hardworking nature. He is extremely passionate about Goa's development," the PM tweeted.
"The entire nation prays for Parrikarji's good health," he added.
Parrikar's family members, BJP workers and his well-wishers held a special prayer at the Mahalaxmi Temple in Panaji in the morning to pray for his health and speedy recovery.
His elder son Utpal Parrikar, along with state BJP spokesperson and former Panaji MLA Siddharth Kunkolienkar, led the prayers at the temple.
Parrikar, who is currently recuperating at his private residence near the state capital, will not celebrate his birthday in public, but the Bharatiya Janata Party has decided to organise various events to mark the occasion.
This is the first time since 1994 that Parrikar is not celebrating his birthday in public after becoming an MLA over two decades ago, Kunkolienkar had said Wednesday.
"Even when he was the Defence minister, he used to fly to the state to celebrate his birthday," said Kunkolienkar, who had resigned from the Panaji Assembly constituency to make way for Parrikar to get elected in 2017.
The BJP's Panaji unit has organised a blood donation camp at party headquarters, which has been a practice since 2006, on the occasion.
Parrikar has been recuperating at his private residence at Dona Paula near here since October 14 when he was discharged from the All India Institute of Medical Sciences (AIIMS).