Davis was selected in the fifth round (163rd overall) by the Green Bay Packers in the 2016 NFL Draft. When asked about his speed the Packers director of football operations Eliot Wolf said, "That was one of the main attractions, definitely." On May 6, 2016, he signed a contract with the Packers. In Week 8 against the Atlanta Falcons, Davis caught his first professional pass on a six-yard pass from quarterback Aaron Rodgers. Later that game, he caught his first career touchdown on a nine-yard pass from Rodgers. He finished the game with three receptions for 24 yards, his total for the whole season.