Monk has guided the Welsh outfit to three victories, including an opening-day 2-1 victory over Manchester United, in the league so far this season.
"It's an honour and privilege, but it's very much a collective – it's not about individuals," said Monk. "For me, it's about the players, myself, the staff around me day-to-day and the staff in the office working hard. This is who I dedicate the award to."
The Swans are currently second in the league table, level on points with leaders Chelsea.