Instead of the suggestions above (edit: I noticed that Bart left this idea in a comment as well), I would suggest making your class more unit testable by making the class accept the input source as a constructor parameter or similar (inject the dependency). A class shouldn't be so coupled to System.in anyway.
If your class is constructed from a Reader, you can just do this:
class SomeUnit {
private final BufferedReader br;
public SomeUnit(Reader r) {
br = new BufferedReader(r);
}
//...
}
//in your real code:
SomeUnit unit = new SomeUnit(new InputStreamReader(System.in));
//in your JUnit test (e.g.):
SomeUnit unit = new SomeUnit(new StringReader("here's the input\nline 2"));