Premier League leaders Manchester City, who were knocked out by Wigan Athletic in the fifth round last season, entertain Rotherham United.
The South Yorkshire duo are among six White Rose sides on the road following a draw made by Ruud Gullit and Paul Ince.
Newcastle United have been drawn at home to Blackburn Rovers in the third round of the FA Cup.
The south coast side were promoted as League Two champions in 2017 and after finishing eighth in League One this season are now leading the way under the guidance of former Wolves boss Kenny Jackett.More news: Bulls fire head coach Hoiberg, promote Boylen
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United will tackle Barnet of the National League at Bramall Lane, while Wednesday will host Luton Town.
Tottenham haven't won a trophy since lifting the League Cup in 2008 and haven't won the FA Cup since 1991 so Mauricio Pochettino will be desperate to try and go all the way this season.
The tie, scheduled for the weekend of January 5, could see midfielder Ryan Woods face his boyhood club competitively for the first time since leaving in 2015.
Norwich have gone out of the FA Cup in the third round in each of the last five seasons, losing in a penalty shootout at Chelsea after taking the Premier League giants to a replay last season.