Q. What is the minimum number of sentences that can be used to make up a paragraph?
A. One.
Of course, a surfeit of one-sentence paragraphs will easily annoy readers, and in expository writing (as opposed to creative writing), most paragraphs will be much more highly developed in order to present and defend an argument.
In many contexts, however, such as newspaper articles or fiction, single-sentence paragraphs can add punch and variety to the writing, and should not be outlawed.