After searching a lot, I couldn't find any ad networks that support displaying ads in a very small size (40*40 square or less pixels).
I saw that applications are able to do so (just like HD camera [picture attached], in the up left corner). After clicking this ad, it goes directly to the google play page.
Is there any ad network that supports this?
The short answer is NO, you can't create small ads like this.
The screenshot you attached is not provided by an ad network.
The smallest ad size supported by most of the ad networks is 320x50.
Usually, developers promote their other applications on their own popular apps, so I guess the ad screenshot you attached must be the ad of the same developer.