Is GFCI protection required for a dedicated exhaust fan circuit?
The National Electrical Code (NEC) does not require bathroom exhaust fans to be GFCI protected, however, there is this bit in Article 110.


  110.3 Examination, Identification, Installation, and Use of Equipment.
  (B) Installation and Use. Listed or labeled equipment shall be installed and used in accordance with any instructions included in the
  listing or labeling.


Which means you have to follow all of the manufacturers instructions while installing the fan. If you read the installation instructions that came with the fan, you might find something like this.


  SUITABLE FOR USE OVER TUB OR SHOWER ENCLOSURE  WHEN INSTALLED IN A
  GFCI PROTECTED BRANCH  CIRCUIT.
  Source


If you install this fan over a tub or shower, the fan must be GFCI protected according to the manufacturer.