The former British Army officer, who turned 100 years old in 2020, was admitted to Bedford Hospital with pneumonia after testing positive for the coronavirus. His family has said he was not eligible to receive the vaccine due to the medication he was on for pneumonia.
Sir Moore's daughter, Hannah Ingram-Moore, announced the news with a message on her father's Twitter.
A number of British stars and politicians have sent Sir Moore messages of support and well wishes in the hours since his family announced his hospitalisation.
Britain's Prime Minister Boris Johnson wished Sir Moore a "full recovery", saying he had "inspired the whole nation" with his efforts in 2020.
Other politicians to send their well wishes include Labour leader Keir Starmer, who wrote: "The whole nation hopes you get well soon @CaptainTomMoore. You've been an inspiration to us all throughout this crisis."
Sadiq Khan, Mayor of London, wrote: "Thank you to our brilliant NHS for taking care of @CaptainTomMoore. Hoping for a speedy recovery and to see Captain Tom back home with his family soon."
Good Morning Britain presenter Piers Morgan was one of the first stars to tweet about the news. He then wrote: "Come on, Captain Sir Tom – we're all rooting for you," along with a photo of the veteran wearing a Union Jack flag as a cape, taken from his British GQ photo shoot.
Britain's Got Talent judge Amanda Holden replied to Sir Moore's tweet, writing: "Goodness me. Wishing you a speedy recovery and look forward to a cup of tea with you when it's safe."
Dr Alex George, the Love Island contestant who is also an NHS emergency doctor, wrote: "My thoughts and prayers go out to Captain Sir Tom Moore, a true hero of these times. Get well soon."
BBC radio presenter Zoe Ball said she was "sending all the love and strength to Captain Sir Tom Moore". While UK children's TV presenter Dave Benson Phillips "wished him a good recovery".
Meanwhile, BBC weatherman Ian Fergusson also said in a tweet he is "wishing a speedy recovery for the inspirational and incredible Sir Captain Tom Moore".