Should I say congratulations to my professor? What is the best way for this?
Professors are people too, hence any acknowledgement of achievements and, as in this case, their part in an achievement is always a nice thing to do.  

It would probably not be a good idea to make too much of a big deal of it - but an email or a chat of congratulations to your professor is a polite acknowledgement and appreciation of a significant achievement.

Most of all, know that you are working with an academic that has, in some way, facilitated a student earning a great award.  Just keep that in mind in all your future interactions with the Professor.