The four-time Super Bowl champion made his 2016 debut on Sunday after serving a four-game suspension as part of the NFL's Deflategate punishment, completing 28 of 40 passes with no interceptions in the 33-13 victory over the Cleveland Browns.
It is the 26th time in Brady's career that he has received the AFC weekly honors -- second in NFL history to the 27 by Peyton Manning.
The NFL on Wednesday also named Arizona Cardinals running back David Johnson as the NFC Offensive Player of the Week for his performance in last Thursday night's 33-21 victory over the San Francisco 49ers.
Johnson had 185 yards from scrimmage, posting 157 rushing yards and two touchdowns on 27 carries to go along with 28 receiving yards on three receptions.
Buffalo Bills cornerback Nickell Robey-Coleman earned the AFC Defensive Player of the Week. He had two interceptions in the 30-19 win over the Los Angeles Rams, including one returned 41 yards for the go-ahead touchdown. He also had a second INT in the waning seconds to seal the victory, Buffalo's third in a row.
Detroit Lions cornerback Darius Slay took the NFC defensive award after forcing two turnovers in the 24-23 win over the Philadelphia Eagles. He had three tackles, one interception, one forced fumble and two pass defenses against the Eagles.
Indianapolis Colts kicker Adam Vinatieri took the AFC special teams honor for the 16th time in his career. In the Colts' 29-23 victory over the Chicago Bears, Vinatieri converted 5 of 5 field goals and two extra points for 17 points. He connected on field goals of 54, 53, 46, 41 and 26 yards to remain a perfect 13 of 13 this season.