My wife, I just have the one, is

A: Those are my wives

B: Well, my wife, I just have the one, ...

This conversation is taken from the series shameless, s07e03, min. 22:47.

What is the meaning of the definite article in B's sentence? I cannot find it in any major dictionary

I would argue that the word "the" is being used for emphasis in this context.

With this sentence structure, it can be hard for the listener to grasp the meaning of those first seven words. The commas make it easy to read, but consider it without the visual cues. Each of the words is monosyllabic and it's an unusual structure.

Adding the "the" for emphasis makes the phrase "I just have the one" something like an idiom.