The Wikipedia page you linked says that sweat is composed of a liquid similar to blood plasma. As all DNA in humans is stored in the nucleus of a cell, it seems unlikely that the sweat itself would contain any DNA.
However, when someone sweats significantly, I can't imagine that no skin cells end up in the sweat. In any case in which this occurs, then the DNA in the cell is in the sweat. Additionally, with small amounts of sweat, I can't imagine how it would be collected without getting any skin cells in it.
This source confirms that sweat contains DNA in some form. Additionally, I think the following quote from here shows that it is stored in cells:
> In every case, what is being tested is the DNA contained in cells of human tissue