"I have tested COVID positive. Shifted to Hospital. Hospital informing authorities, family and staff undergone tests, results awaited," Amitabh, 77, tweeted.
"All that have been in close proximity to me in the last 10 days are requested to please get themselves tested," he added.
Abhishek, 44, said both his father and he had had mild symptoms and requested everybody to be calm and not panic.
"Earlier today both my father and I tested positive for
Bollywood celebrities, including Madhuri Dixit-Nene, Taapsee Pannu, Sonam Kapoor Ahuja, Shahid Kapoor, Riteish Deshmukh among others took to Twitter and wished the duo good health.
Amitabh's "Pink" co-star Taapsee wrote, "And you shall be back to health and happiness soon... champ!"
Madhuri hoped for a quick recover of the veteran star.
"Wishing you speedy recovery Amit ji," she wrote. Filmmaker Hansal Mehta said he was "praying" for the megastar's "early recovery."
Actor Shahid Kapoor posted on the microblogging site, "Wishing you the speediest recovery Amitji and Abhishek. Wishing the entire family the best of health. Much love."
"Take care sir. Love you. Awaiting your tweet when you say you're fine & going back home," wrote filmmaker Kunal Kohli.
Director Sudhir Mishra tweeted, "What a man ! Look at the matter of fact way he announces . So correct . Nothing will happen to him . He's been through tougher times . Prayers for the speedy recovery of Amitji and Abhishek."
"Get well soon sir," said veteran Malayalam actor Mammootty.
Actor Bipasha Basu said she was praying for speedy recovery.
South superstar Mahesh Babu and Dulquer Salmaan as well as actors Pankaj Tripathi, Nimrat Kaur and Rajkummar Rao were among those who sent him their wishes.
"Get well soon Amit uncle. All my love and prayers," actor Sonam Kapoor replied on his tweet.
Actor Riteish Deshmukh said he's praying for the family's health.
"Get well soon my brother - @juniorbachchan - praying for the family's well-being and good health- love you man," the actor wrote.
Veteran actor-host Simi Garewal said she is sure the father-son duo will be fine soon.
"Dearest Abhishek..so so sorry to hear about this - but I know you both will be fit and fine soon - you have our prayers and love to see you through,"she tweeted.
Actor Preity Zinta said,"Get well soon Amitji Praying for your speedy recovery. Love you loads @SrBachchan"
Actor Vicky Kaushal also wished good health to the duo.
"Get well soon AB. Wishing you and @SrBachchan Sir a very speedy recovery," he wrote.
Amitabh was last seen in Shoojit Sircar's "Gulabo Sitabo", which released on streaming platform Amazon Prime Video last month.
Abhishek made his digital debut on Friday with Amazon's "Breathe: Into the Shadows". The actor's performance in the series is receiving positive reviews. JUR SHD SHD SHD