Leadership skills are an important aspect of mechanical engineering careers, at least in my experience. I work as a Project Manager in the manufacturing industry and have found that leadership is one set of skills that wasn't valued as much at my school. I think it is important that colleges and universities provide Mechanical Engineering students with a leadership and management background to some extent, because many students will go on to use these skills in their industry of choice.
If you are still looking into colleges or universities, research their programs and find out if they place an emphasis on leadership. Talk to academic advisors to learn more about other opportunities for leadership development. If you're already in college and your school, like mine, doesn't place a strong emphasis on leadership, look for internship opportunities in which you will be given the chance to supervise others and build management skills that way.