The Canaries are the only side involved in the draw who were in the Premier League last season.
Fellow relegated sides Bournemouth and Watford will join the competition in the next round, along with other top flight clubs not involved in European competition.
Newport meet Swansea at Rodney Parade in a Welsh derby and new Birmingham boss Aitor Karanka will face Cambridge at St Andrew's.
Cardiff, who lost in the Sky Bet Championship play-offs last season, head to Northampton and Millwall travel to Crawley.
Dean Holden welcomes Exeter in his first game as permanent Bristol City manager and Paul Lambert's Ipswich play Bristol Rovers at Portman Road.
In the northern section, Harrogate will travel to Tranmere for their first involvement in the competition after promotion from the National League last season.
Fellow promoted side Barrow head to Championship side Derby while Stoke have been drawn at home to Blackpool.
Sheffield Wednesday travel to Walsall, Huddersfield go to Rochdale while Blackburn, the 2002 winners, will host Doncaster.
Wigan, relegated to Sky Bet League One after going into administration, head to Fleetwood and Nottingham Forest visit Barnsley.
Preston host Mansfield, Huddersfield go to Rochdale and Middlesbrough welcome Shrewsbury.
The ties are scheduled to be played over the weekend of the 5-6th of September.
The competition will open the season for clubs with the league campaigns starting on 12 September.
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