Q:

May I drop "is" in constructions like "as is shown by the example of..."? 

May I drop "is" in constructions like "as is shown by the example of..."? 
On the one hand, such reduced variants can be met even in Wikipedia.  But on the other hand, I don't quite understand its grammatical structure. 

A:

Rather than being a reduced variant, as is shown by in your example "as is shown by the example of" is an expanded variant! 
The verb is is superfluous in the construction you present, and so is not omitted in as shown by the example.  This is a common and proper use of as in its rôle as an adverb with the meaning "in the manner."  See Dictionary.com, definition 4: She sang as promised.  He left as agreed. 
Your example phrase could thus be written as:

...in the manner/as is shown by the example of...

In commentary, you suggested another example:

The body's mass is constant as was established by Newton. 

Likewise, "was" is superfluous here, and the sentence could be written as:

The body's mass is constant in the manner/as was established by Newton. 

It may be possible to make the case for an ellipsis of the verb "is" (as your question suggests) but many writers prefer a solution which uses the fewest words. 
p.s.:  The comma clarifies the meaning of either usage:

The body's mass is constant, in the manner established by Newton. 
  The body's mass is constant, as (was) established by Newton.