In Harry's fifth year, while Professor Snape is being assessed by Dolores Umbridge, the class is making the Strengthening Solution and Umbridge expresses some concerns as to its suitability:
"Well, the class seem fairly advanced for their level," she [Umbridge] said briskly to Snape's back. "Though I would question whether it is advisable to teach them a potion like the Strengthening Solution. I think the Ministry would prefer it if that was removed from the syllabus."
Harry Potter and the Order of the Phoenix, Chapter Seventeen - Educational Decree Number Twenty-four
The Wikia (unreliable as we all know it can be) speculates that it "presumably increases the drinker's strength." That's a possibility, though considering at that particular time their (or at least Fudge's) greatest fear was that Dumbledore was using Hogwarts to train his own personal army, it doesn't seem like it would be particularly troubling for the Ministry if that's all it did. After all, in a magical battle against trained Aurors and other Ministry workers, an increase in physical strength likely wouldn't give much advantage (if any at all); Hagrid, while obviously exceptionally strong, appeared to get all of his magical resistance from having giant's blood from his mother.
So is there any canon information on what this potion does? Canon being the seven Harry Potter books, the officially released supplementary books, JKR quotes and interviews, and Pottermore.
If there turns out to be a lack of canon information (which I suspect may be the case), I'd also consider accepting a particularly well reasoned argument as to why my above assumption is incorrect and a potion that merely increases physical strength would be of particular worry to the Ministry at that time.