Lifeline Hellas, a Greek missing persons charity, issued a Silver Alert after the police were unable to locate her.
The charity’s alert said: “Her life is in danger. If you know anything, contact the Silver Alert service, 24 hours a day, at the National SOS Line 1065.”
Bourda is described as having straight blonde hair down to her shoulders, hazel eyes, 5ft 6in tall and of slim build.
The Hellenic Coastguard is reportedly conducting a search operation at sea and investigating reports that her belongings were left on the beach.
Three recreational craft, five fishing boats and two patrol boats were involved in the search, according to Sky News.
Local media reported that Bourda lived with her husband, who is thought to be of Greek origin, in Serres, Macedonia.
The British embassy in Greece shared a notice on Facebook which read: “Michele Ann Bourda went missing on August 1, 2025, at the beach of Ofrynio in Kavala.
“On the day she went missing, she was wearing a swimsuit with decorative stones, yellow water shoes and red plastic sunglasses. Her life is in danger.”
It comes after a 60-year-old British tourist went missing while on holiday in the country last month.
He was last seen in Tristomo, a village on the island of Karpathos, and his car was abandoned in 38C heat.
Michael Mosley, the television doctor, died after going missing while walking on the Greek island of Symi last summer.
The broadcaster and columnist’s body was found after a four-day search in June 2024. CCTV footage appeared to show him falling over close to where his body was eventually located.
Crispin Butler, the senior coroner for Buckinghamshire, said that Mosley’s death was “most likely attributable either to heatstroke (accidental) or [a] non-identified pathological cause”.
Meanwhile, a 48-year-old British tourist was found dead after going missing on Theologos beach on the island of Rhodes.
He was reported to have been on holiday with his family and went for a swim with his niece, who left early to return to the hotel.