The World War Two veteran became a national hero by raising more than £32m for the NHS during the first coronavirus lockdown.
A 35-year-old man has been charged over an alleged offensive tweet about Captain Sir Tom Moore, police have said.
A Police Scotland spokeswoman said: "On Friday 5 February 2021, we received a report of an offensive tweet about Captain Sir Tom Moore who died on Tuesday 2 February.
"A 35-year-old man has subsequently been arrested and charged in connection with communication offences and is due to appear at Lanark Sheriff Court on Wednesday 17 February."
Capt Sir Tom, who captured the hearts of the nation with his fundraising efforts during the first coronavirus lockdown, died in Bedford Hospital last Tuesday, after contracting COVID-19.
The Second World War veteran's family said the last year of the 100-year-old's life was "nothing short of remarkable" and that he had "experienced things he'd only ever dreamed of".
In July, he was knighted by the Queen for his efforts. Her Majesty sent a private message of condolence to his family after his death, while the Union flags above 10 Downing Street flew at half-mast.
The day after, a national clap was held in his memory, something his family said they were "incredibly touched" by.
