Here is the back of the MM:
http://images.apple.com/mac-mini/images/specs_ports.jpg
Unfortunately for you, it seems like you will need an adapter for it to work. The only adapter that ships with the MM is the HDMI-DVI option.
I don't see any way for to avoid getting an adapter. Would I be correct in assuming that you have a display port cable? If so, I would look for a mini-displayport to displayport.