1) Since you are not asked to enter a day of onset, just a month and a year, technically, you can enter the activity so long as you wait until it's June to fill in the space. If you try to put a June 2017 start date in now, the program will refuse to Save it.
2) That said, I am not a fan of including experiences with brief involvement, as they do not enhance your application. I do understand wanting schools to know your plans though.
Some strategies to consider so as not to appear to be adding fluff:
*1) Mention it at the end of the PS if you can make it seem like a next logical move in your journey to medicine or
*2) add it at the end of a related activity, explaining that one experience had the impact of inspiring xxx, and you've been accepted to start an Internship in Yyy on (date) to explore . . . .
*3) Use an Honors/Awards space to discuss your acceptance into the Internship and how selective the process was, with expected start date, location, duties, etc.
*4) Save it for update letters later in the cycle so you have something fresh to say (where allowed).