Brown and fellow defensive backfield mate Antrel Rolle have both been honored in the past three weeks.
Brown intercepted Cowboys quarterback twice, moving his season total to five. He also recovered a fumble and led the Giants in tackles with six.
This is the second year in a row in which two different Giants defenders have won Defensive Player of the Week. Last year, Mathias Kiwanuka won the award in Week 9, while Jason Pierre-Paul took it home Weeks 14 and 16.