It depends on how you define sentence and then how you define shortest. The answer does not appear to be Go, though (although that's quite a good shot at an answer).

The question uses the phrase complete sentence from which we can probably assume that the Original Poster is referring to a fully grammatical utterance headed by a finite verb.

With regards to shortest, there are at least two ways we could measure this. We could do it orthographically, in which case the sentence with the fewest letters would probably be the imperative of the verb 'X' (pronounced /eks/). Although usually used transitively, as in the Mark Twain quote:

'I shell have to x this ere paragrab,' said he to himself, as he read it over.'

... it could easily be used intransitively too:

A. What shall I do now?

B. X! [meaning "start crossing out"]

However, although 'X' contains only one orthographic symbol, in terms of sound it consists of three segments: /eks/. So, if by shortest sentence, we mean shortest in terms of segments, then this word wouldn't do. The sentence Go has one consonant sound plus a diphthong - /gəʊ/ in Southern standard British English and /goʊ/ in General American. We could regard this as having either two or three segments. However, it is plainly obvious that this could be shorter. The reason is we also have a verb owe which has exactly the same sound without the /g/, namely /əʊ/ or /oʊ/. However, it is quite hard to use this verb without a following complement, and so an imperative sentence might be a bit implausible: Owe!.

A better contender in terms of segments might be the verb OOH meaning to make an ooh sound, as in the audience oohed and aahed. So if you were in the audience at one of those sitcoms where the audience were directed to laugh, clap, ooh and aah, one of the directions you might get, could feasibly be the imperative:

Ooh!

This fully complete one word sentence consists only of the one vowel. In phonemic script it looks like this: /u:/. This then might be a contender for the shortest sentence in English. But of course there are others. For example there is always:

Aah!

... which looks like this: /a:/!