Does the word "units" have a valid abbreviation?
In materiel management these distinct concepts of "unit" are called the "Unit of Measure" (U/M or UOM) and "Unit of Issue" (U/I or UOI), but these terms may be unfamiliar to some.
ORIGINAL ANSWER assumed a medical context, kept here for posterity:
In a medical context, I'd be careful not to use any abbreviations that could be ambiguous. In particular, there is another meaning of the word "units" in pharmacy:
Unit 1 - a category of measurements, like kilograms, and miles.
Unit 2 - piece, item
Unit 3 - abbreviated U, or often International Unit (IU), an "unit of measurement for the amount of a substance, based on biological activity or effect." Different drugs have different-sized U's.
If you were to use the abbreviation U you might run into confusion with the last definition.
Well, in a medical context, you have IU, International Units, which hilariously varies according to the substance in question. So it would be perfectly reasonable to see "IU: [Milligrams]", specifying that the IU for this substance is milligrams. And it's also common practice to simply use U rather than IU, though opinions as to the validity of this vary. So if you're asking about a display you're seeing, I would think that's what's meant.