Arsenal won three of their four league games in the month, with the one they did not win being their 4-4 draw at Newcastle, a match they had led 4-0 with 22 minutes remaining.
It is the 11th time that Wenger has won the award.
West Ham midfielder Parker enjoyed a fine month, helping the Hammers haul themselves off the foot of the table with stellar performances in their 3-1 wins over Blackpool and Liverpool.
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Arsene Wenger And Scott Parker Win Awards