Pip Holmes, reportedly a 45-year-old artist from Cornwall, was one of five foreigners paraded at a news conference last week in Denpasar, the capital of Bali province.
Indonesian police said he received nearly 31kg of cannabis oil in the mail and could face the death penalty if convicted.
Mr Holmes, who describes himself as an artist and surfer, claims he was caught with just a tiny amount – around 3g – of medicinal THC oil, which he uses to treat his arthritis.
His family has launched a crowdfunding page to raise $100,000 (nearly £80,000) for legal fees to keep the father-of-two out of prison.
They say he could face a jail sentence of between five and 15 years but are hoping he can instead serve a short spell in a rehabilitation centre before being deported to the UK.
A message from Mr Holmes on the crowdfunding site said he had already been moved from a cramped police cell in Bali to a rehabilitation centre and has been helped by messages of support from his family.
“For the last few days, each morning I have woken up in a terrible nightmare. I still can’t believe that I’m here and I feel sick with fear,” he said.
“As it stands, I don’t know if I’m about to spend a few months in a rehabilitation or if I’m about to face five to 15 years in Kerobokan – one of the toughest prisons on earth.”
Mr Holmes said he had been in Bali for two months before his arrest on 3 December.
“It all went terribly wrong when I was arrested for possession of a tiny amount of THC oil. Stupid much? Yes very very stupid. Right now I feel helpless and very alone,” he said.
“This is Asia, it’s not like the west. I am guilty under Indonesian law of possession of narcotics, there’s no denying that.
“Even though medicinal THC is something so widely accepted elsewhere and it was such a small amount, I foolishly crossed the line in a very strict country.
“The only way now to ensure my sentence is something I will survive is to invest in the right legal representation and rehabilitation.”
Doctors have been able to prescribe medicinal cannabis products to patients in the UK since 1 November after the drug was rescheduled.
However, Indonesia has strict drug laws and dozens of convicted smugglers are on death row.
British woman Lindsay Sandiford, from Cheltenham, was convicted of drug-smuggling offences and sentenced to death in 2013.
A Foreign and Commonwealth Office spokesman said: “Our staff are assisting a British man following his arrest in Bali, and are in contact with his family, lawyer and the Indonesian authorities.”
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