"Birthday wishes in person for the Emir. PM Narendra Modi conveys his greetings at the start of official talks," External Affairs Ministry spokesperson Vikas Swarup tweeted along with a photo.
British-educated Sheikh Tamim, who turned 36 on June 6, came to power after his father Sheikh Hamad bin Khalifa Al Thani announced his abdication as leader of the gas-rich Gulf state in June 2013.
Born in Doha, he is the fourth son of Sheikh Hamad and became Qatar's heir apparent in 2003 after his older brother Jasim renounced his claim to the throne.
On the second leg of his five-nation tour, Modi arrived here yesterday on a two-day visit which is focused on giving a new push to the economic ties, particularly in the hydrocarbon sector, between India and Qatar.