A family spokesperson said that the pneumonia had meant that Moore was not able to receive a dose of the Covid-19 vaccine.
Some online have questioned the wisdom of the December 11 Barbados trip, which took place before the UK went back into strict lockdown and while there was a travel corridor with the island.
The hosts of popular British breakfast television show This Morning defended Moore and his family, labelling his detractors as "trolls".
Broadcaster Julia Hartley-Brewer, who joined Phillip Schofield and Holly Willoughby on This Morning, said: "I was stunned to see some trolls on social media saying: 'Oh, if he didn't go to Barbados!' 'He went on a lovely, warm, perfectly legal Caribbean holiday with his family, and I think that's absolutely wonderful he did that, and nothing whatsoever to do with his ailments now.
"I do think the trolls need to take a day off."
Schofield agreed, saying critics should "just sod off".
Piers Morgan responded to the controversy on Twitter, where the television host and former newspaper editor said that Moore "helped save Britain" and "his trolls shame Britain".
Moore's fundraising efforts raised more than £32 million ($61m) for the NHS, walking 100 laps of his garden before his 100th birthday during the UK's first national lockdown in April.
The veteran set out to raise £1000 from his lockdown charity challenge but his efforts struck a chord with the nation, and praise and donations flooded in.
In acknowledgement of his efforts, he was knighted by the Queen during a unique open-air ceremony at Windsor Castle.
