Most of my friends who have done MSc in Engineering are going to consultancies these days. I want to know if you must have a Masters degree to do so. Is it possible for those who have completed high school also take a similar training and get job through consultancies?

You don't need any degree to join consultancy.once u graduate from the college put your degree inside your luggage and join the consultancy.

Ofcourse you don't need Engineering for IT. However, if you don't have a citizenship or PR, then to get a work visa (H1B), you'd need undergraduate degree to get the visa. Having a master helps even more; just doesn't have to be in Engineering.