There were no massage parlors when when I was in Moscow last time, about 15 years ago, but sure as hell a lot has changed. I'd dare to say that almost all of the prostitutes there will tickle you for the right amount of dollars.
Just be careful when you go there, practically all the red light business is in the hands of the Russian mafia. Ask a taxi driver for the right place to go, but don't let him drive you there before you've handed an envelope with the address to the hotel reception, telling them to open it if you don't return after a certain span of time. They're also into Mickey Finn's there (drugged drinks), so be careful.