I think the OP is doing some sort of homework, so it's not really important that the code accounts for all sorts of technical limitations. Ideally, there shouldn't be a limit on how long list of arguments a function can take. I think different Lisp implementations may differ in this regard as well. And, I assumed that the minimum function was the min - I think, I've at least a 50% chance of guessing that right
Besides reduce the OP could also use any kind of loop, or call min recursively using some improvised Y-combinator function etc. I didn't really mean that the last example is the only right, rather an alternative way to solve the problem. Although, yeah, if, for whatever reason I really needed that kind of functionality, I'd stick with reduce.