According to police, small-time operations pay a bribe of around $8,000 to win a construction licence without any requisite papers, the Vremya Novostei daily reported on Friday.
They are then hired out by legal construction firms for jobs, before disappearing without paying any taxes or taking any responsibility for potentially poor work.
Police launched their investigation shortly after the roof of an indoor swimming pool in Moscow collapsed in February, killing 28 and injuring 110 people.
Investigators found that while the major constructors involved could be reached, their subsidiaries no longer existed.
The Moscow city government is closely linked to construction projects in the Russian capital, with the mayor's billionaire wife running a construction firm.
Besides the potential construction problems, the unpaid taxes cost state coffers $1 billion a year, the Vedomosti business daily reported, quoting investigators.
The construction business is currently booming in Moscow; old - and some historic - buildings being torn down to be replaced by exclusive apartments and office buildings.