There are two districts (Amphoe) in Thailand which have just one Subdistrict (Tambon), and another four districts in Bangkok (Khet) which have one subdistrict (Khwaeng). As the two kinds of subdistricts are quite different in their functions, I'll write something about the Bangkok districts later.
The two districts are Ko Sichang of Chonburi province - an island off the coast - and Mae Poen in Nakhon Sawan province, a remote part of the province including mountain area. Both district have a quite different history - whereas Ko Sichang already was a minor district with just one subdistrict in 1943, when it was reassigned from Samut Prakan to Chonburi province, Mae Poen was created in 1996, and its single subdistrict Mae Poen was just created shortly before in 1992. Maybe the fact that this district was created directly at the time when the creation of new Tambon stopped altogether explains why it remained with one subdistrict. Looking into the history of other districts, there are a few more which originally had just one subdistrict when they were established as a minor district (King Amphoe).
- Soeng Sang, Nakhon Ratchasima. Created in 1976 with the single subdistrict Sa Takhian, the second subdistrict was created in 1977. The minor district was upgraded in 1979, and today has six subdistricts.
- Than To, Yala. Created 1975 with the single subdistrict Mae Wat, the second subdistrict was created in 1977. Today the district has four subdistricts and became a full district in 1981.
- Pa Daet, Chiang Rai. Created in 1969 with the single subdistrict Pa Daet. In 1970, two new subdistricts were created. 1975 it was upgraded to a full district, and today it has five subdistricts.
- Ban Kruat, Buriram. Created in 1939 with the single subdistrict Ban Kruat. As the Royal Gazette is unreliable for the subdistrict creations before 1950, I can only say the district was upgraded in 1965 and has nine subdistricts today
I don't know whether there were any official rules predating those defined in 2003 by the cabinet on how many subdistricts are necessary for a new minor district, but even the 2003 rules allowed to overrule the minimum of three if there is a special need for the creation of a new district.
Already before the decentralization with the creation of the Subdistrict Administrative Organizations, the Tambon had a limited local representation of the population by the elected headman. I don't know whether there were any minimum requirements for a subdistrict in terms of population of number of administrative villages, Ko Sichang with a population of less than 5000 people never qualified for a second subdistrict. But its remoteness on an island made sense to have a district office as the government office which normal citizens have to visit most.