The move by the state postal agency is part of its drive to increase revenue, said Anusra Chittmittrapap, president of Thailand Post.
Customers living in Bangkok will receive their prescriptions in one day, while for those in the provinces it will take three to five days.
Udom Kachintorn, a clinical professor of medicine at Siriraj Hospital, said the facility has 8,000 to 9,000 patients each day waiting to pick up medicine.
Ms Anusra said Thailand Post linked its back-end system to support back-office applications with Siriraj Hospital, enabling access to patients' personal information, contact numbers and addresses listed with the hospital.
The service is a flat rate of 150 baht nationwide.
After launching a pilot project in March, Thailand Post now has 300 customers using its medicine delivery service. "We will soon expand our delivery services to other hospitals," she added.
Ms Anusra said the plan is to enlarge the scope of its delivery services to the healthcare industry, including laboratory tests and medical equipment for private hospitals.
"Health care is a promising new revenue stream for us, apart from banks and financial institutes," she said.
Thailand has high potential to become a medical hub in Asean, so the country needs to have high-quality logistics and delivery services to promote the healthcare industry, said Ms Anusra.
Ms Anusra said Thailand Post, through subsidiary Thailand Post Distribution, will start providing logistics service in July to capitalise on surging demand for door-to-door delivery services. The company has 350 million baht in registered capital.