Stalin said this after some "miscreants" shared false information about the DMK chief's condition, who is being treated for fever.
"There is good improvement in his health, the fever and infection is receding," PTI quoted Stalin as saying.
Earlier in the day, Stalin thanked President Ram Nath Kovind, Prime Minister Narendra Modi, Congress President Rahul Gandhi and others for enquiring about the health of his father and party President M.Karunanidhi.
Stalin tweeted "On behalf of the DMK, I thank @rashtrapatibhvn and @PMOIndia for their enquiries about @kalaignar89's health.
"I am extremely grateful for their offers of help. Thalaivar is getting the best medical care and treatment. We hope he will recover soon and thank everyone in his own words."
Party workers began arriving at Karunanidhi's residence after Kauvery Hospital, which is providing medical treatment for the leader, said in a bulletin last night that there has been a "slight decline" in his health.
MDMK chief Vaiko, Tamil Nadu BJP chief Tamilisai Soundararajan, CPI leader D Pandian and Tamizhaga Vazhvurimai Katchi leader Velmurugan visited the residence and enquired about his health from family members and Stalin.
(With inputs from agencies)