Mr Thakor, 23, has been suspended on full pay over two allegations said to have happened in June.
Police confirmed a 23-year-old had been arrested in connection with "an ongoing investigation into incidents of sexual exposure".
Derbyshire Cricket Club have previously said the all-rounder was not on club duty at the time.
Derbyshire Police said it received reports a man had indecently exposed himself to women on two separate occasions at a housing development off Radbourne Lane, in Mackworth.
Mr Thakor joined Derbyshire after rejecting a new contract with home county Leicestershire in 2014 and signed a new three-year deal in August 2016.
Derbyshire cricketer Shiv Thakor has been arrested on suspicion of indecent exposure.