Smith put together one of the best games of his career in Kansas City's 42-27 victory over the New England Patriots, completing 28 of 35 passes for 368 yards and four touchdowns to earn the AFC honor announced by the league on Wednesday.
Bradford was named NFC Offensive Player of the Week for his performance against the New Orleans Saints, going 27 of 32 for 346 yards with three touchdowns en route to a 29-19 win.
Jacksonville Jaguars defensive end Calais Campbell took the AFC Defensive Player of the Week honor, setting a franchise record with four sacks in a 29-7 victory over the Houston Texans.
Los Angeles Rams cornerback Trumaine Johnson earned the NFC defensive award, returning an interception 39 yards for a score and forced a fumble in the 46-9 victory over the Indianapolis Colts.
The AFC Special Teams Player of the Week went to Oakland Raiders kicker Giorgio Tavecchio, who made all four field-goal attempts in the 26-16 win over the Tennessee Titans while subbing for the injured Sebastian Janikowski.
Detroit Lions kicker Matt Prater was named the NFC Special Teams Player of the Week after making a 58-yard field goal and filling in as an emergency punter in the 35-23 win against the Arizona Cardinals. Prater punted four times after Lions punter Kasey Redfern was hurt.