The 100-year-old was admitted to Bedford Hospital yesterday (31/01) as he needed help with his breathing.
Captain Moore's admission came after he tested positive for Covid-19 last week.
Prior to that, he had been treated at home for pneumonia.
In a statement released by Bedford Hospital with the family's permission, the hospital said that they continue to care for him.
Bedford Hospital said: "Bedford Hospital continues to care for Captain Sir Tom Moore.
"At this time members of Captain Tom’s family are with him.
"We respectfully request that media give the family space and privacy and do not contact them directly so they can focus on their father, grand-father and father-in-law."
In a tweet yesterday about her father admission to hospital on Captain Moore's Twitter account, his daughter Hannah Ingram-Moore, praised the medical care he had received at home for pneumonia.
She also said: "We know that the wonderful staff at Bedford Hospital will do all they can to make him comfortable and hopefully return home as soon as possible."
Thousands of people online have wished Captain Sir Tom Moore well including Prime Minister Boris Johnson.
He tweeted: "My thoughts are very much with @CaptainTomMoore and his family. You’ve inspired the whole nation, and I know we are all wishing you a full recovery."
