Is this sentence correct?
The only countries from South America that I know are Mexico, Brazil and Argentina.
Is not 'the only' meant for just only only one?
Is this sentence correct?
The only countries from South America that I know are Mexico, Brazil and Argentina.
Is not 'the only' meant for just only only one?
This is totally normal usage - because 'countries' is (massively) plural, it is obvious to a native speaker that a short list still fits the definition of 'only a few'.
Your example is fine. It is perfectly good idiomatic English to use "the only" to list one or more of a larger set. So your sentence is correct although it may be better to change the preposition:
The only countries in South America that I know are Mexico, Brazil and Argentina.