My 13 year old boy suddenly has small boobs. What is it?
What can I do to reduce them? It is socially very unconfortable for him.

Its called diet and exercise. Id say if he is at the point of developing breasts already all exercises would be good for him but you should do a lot of push ups(in different styles, going to find a link to show you what I'm talking about on the push ups)

Another great option is martial arts or some other form of self defense.

As a side note, in any type of upper body exercise the "boobs" will get bigger as muscle builds beneath them for a short while.

Also for what your looking to do I recommend "diamond", "normal", "wide" and one type not shown where in a normal or wide stance, instead of your hands facing forward they face at either a 45 degree or 90 degree angle away from the body on each side so if hands normally look like || they should look like \/ or
- -, this allows a lot of different muscle groups to be worked out in the chest arms and back. Doing these sort of pushups on an incline(with feet or hands on a chair) is also a good thing, but that should come much later into the exercise plan(assuming 4 45 minute workouts a week, say 2 months you should add some incline).

The reason I suggest martial arts, is that it can be very hard to get motivated for diet and exercise on your own or even a family basis, but if your in a fun environment where exercise is a byproduct of another activity you don't notice it as much and get in shape at the same time.

Link for 19 different push ups
19 Push Ups Variations Without Any Equipment Video