Van Persie scooped the award after helping the Gunners stay unbeaten throughout the month, chipping in with five goals and two assists.
The 26-year-old Dutchman has now won the award for a second time, having previously claimed the prize in November 2005.
Hodgson picked up October's Manager of the Month award after guiding the Cottagers through an unbeaten month despite a tricky fixture list, which included a fine 3-1 win over Liverpool.
This is the third time Hodgson has won the monthly gong and comes almost twelve years since he last scooped the prize in December 1997, while manager of Blackburn Rovers. He also won the award in August 1997.
Andrew Southwick, Goal.com