The offer price was at a discount to Tuesday's closing price of Rs 514.35 on the BSE but higher than the Rs 340 it had paid for the shares in 2013.
Airtel closed 3.73 per cent lower at Rs 495.15 on the BSE on Wednesday.
In a regulatory filing, Three Pillars Pte Ltd confirmed the sale, saying 19.98 crore sales were sold through the open market.
The buyers included a mix of foreign and domestic institutional investors, said another source who did not wish to be named.
The company now holds nil shares in Bharti Airtel. It did not immediately give the price at which the sale was made.
A Bharti Airtel spokesperson declined to comment on the stake sale by the Qatari investor.
Qatar is redeploying resources to bolster the economy and banking system after Saudi Arabia, the United Arab Emirates and Bahrain cut diplomatic ties over charges of funding terrorism. Qatar has repeatedly denied the allegations.
Qatar Foundation Endowment had acquired the 5 per cent equity stake in Bharti Airtel for Rs 6,796 crore way back in 2013.
The stake sale coincides with similar moves by other Qatar-based investors who are paring their holdings in various foreign companies in the backdrop of sanctions imposed by Arab countries.
The stake sale also comes at a time when the Indian telecom market has seen an intense tariff war triggered by the entry of aggressive newcomer Reliance Jio, backed by billionaire Mukesh Ambani, in 2016.
The competition in the market has hit earnings and financial metrics of large established telecom players and led to a massive consolidation in the industry, with smaller players exiting the market, and others either joining hands or acquiring smaller players to protect their turf.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)