Charles cancelled a busy program scheduled in Birmingham on Friday to prioritise his recovery after experiencing "temporary side effects" from his cancer treatment.
He sent a message addressed to "the people of Myanmar" on Saturday.
In his message posted on social media, Charles spoke of his and Queen Camilla's shock and sadness after a deadly 7.7 magnitude earthquake struck Myanmar at midday local time on Friday.
The quake has claimed more than 1600 lives and injured thousands of people, according to the country's military junta government.
Myanmar is a former British colony.
"My wife and I were most dreadfully shocked and saddened to learn of the devastating earthquake in Myanmar, with its tragic loss of life and appalling damage to homes, buildings and livelihoods, not to mention the destruction of sacred pagodas, monasteries and other places of worship," King Charles said.
"I know that the people of Myanmar continue to endure so much hardship and tragedy in your lives, and I have long admired your extraordinary resilience and spirit."
He sent his deepest possible sympathy to all those who have suffered the profound tragedy of losing their loved ones, their homes and livelihoods.
The earthquake that struck Myanmar had an epicentre near Mandalay, the country's second biggest city, sending buildings in many areas toppling to the ground and causing widespread damage.
The earthquake also shook neighbouring Thailand, killing at least nine people. A partially built high-rise collapsed in Bangkok.
Another 47 people were still missing, authorities said on Saturday.
Charles, 76, is understood to be staying at his Highgrove estate in Gloucestershire after it was revealed he had been in hospital with side effects from his cancer treatment.
Buckingham Palace announced on Thursday night that the King "required a short period of observation in hospital" earlier that day.
The monarch appeared in good spirits on Friday morning as he was seen leaving Clarence House in London in a black Audi.
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