This was the first meeting between the two leaders after Modi became the prime minister in May 2014. The meeting at Karunanidhi's Gopalapuram residence during which Modi enquired about his health lasted about 20 minutes.
Modi sat next to wheelchair-bound Karunanidhi, 93, and held his hands.
"Met former Tamil Nadu CM, Thiru M Karunanidhi and enquired about his health.@kalaignar89," Modi wrote on his official Twitter page. The opposition DMK indicated that not much should be read of the meeting and that it was a "courtesy call."
"The prime minister did not come with any political intentions nor did he talk politics. He only enquired about Kalaignar's (Karunanidhi) health," M K Stalin, who is Karunanidhi's son and DMK working president, told reporters.
Modi called on Karunanidhi as he was a senior Dravidian leader and only came to enquire about his health, he said. The DMK leader said only the media was thinking that there was a political angle to today's meeting.
"Kalaignar (Karunanidhi) is a very senior leader in Indian politics. Mr. Modi has respect for Kalaignar," DMK spokesperson T K S Elangovan said.
He said in the past when both were chief ministers, they used to greet each other during meetings in Delhi and this has been the practice.
"This is a courtesy call," he said, adding, the meeting was only to greet the leader who is recuperating.
Stalin welcomed Modi at the gate of the residence and honoured him with a red shawl. Stalin, also Leader of the Opposition in the state Assembly, on his official Twitter page said that Modi during the meeting wished Karunanidhi a "speedy and full recovery."
"Hon'ble PM @narendramodi made a courtesy call on Dr @kalaignar89...The PM enquired about his health & wished him a speedy & full recovery," Stalin wrote.
During his visit, Modi was accompanied by state Governor Banwarilal Purohit, Defence Minister Nirmala Sitharaman, Minister of State for Shipping Pon Radhakrishnan and state BJP chief Tamilisai Soundararajan.
Soundarrajan told reporters that the prime minister invited Karunanidhi to visit Delhi.
DMK leaders, including Kanimozhi, who is the daughter of Karunanidhi and a Rajya Sabha MP, were among those present during the meeting.
Later, Karunanidhi made a brief appearance outside and waved at his supporters who cheered him.
Karunanidhi, who was taken ill in October 2016 due to a drug-induced allergy, was twice admitted to a private hospital in December last.
He has been since confined to his house but made one rare appearance on October 19 this year when he visited an exhibition here held to showcase the 75-year journey of DMK'smouthpiece, 'Murasoli.