The former Michigan product completed 23-of-26 passes for 267 yards with four touchdowns in last Sunday's 35-7 rout of the Jacksonville Jaguars.
His 88.5 completion percentage established a single-game franchise record and it was the 12th time in his NFL career he has thrown at least four touchdown passes in one contest.
Woodley recorded two sacks, one forced fumble and 10 tackles in the Steelers' 23-20 win over the Baltimore Ravens.
Smith, also a back-up quarterback, scored on a 106-yard kickoff return, the longest play in Jets history, helping New York record a 29-15 win at previously unbeaten Indianapolis.
Woodley and Smith are first-time weekly honorees.