Leicester City stand between the Canaries and their first FA Cup quarter-final appearance for 20 years.
Sunday's fifth round draw gave Paul Lambert's men a home tie against the Championship club on the weekend of February 18 and 19.
Norwich City doubled the Foxes on the way to promotion last season with a thrilling 4-3 victory at Carrow Road and a 3-2 success in the return fixture.
Leicester earned a place in the last 16 with a 2-0 home victory over Swindon on Saturday, Jermaine Beckford scoring both goals for Nigel Pearson's team.
'It's a home tie and I think that's all you ever look for in a cup draw, regardless of what the opposition was going to be,' said Lambert. 'It was always going to be hard but being drawn at home is good for us.
'We played them twice last year in two really tough games, although it's a new manager now. It'll be a really tough game but it's one we'll look to go and win.'
Winning clubs in the fifth round will each receive �180,000 from the FA's prize fund.
The Canaries are in the fifth round for only the fourth time in 20 seasons after Saturday's 2-1 win at West Bromwich Albion.
And they last reached the quarter-final stage in 1992, going on to the semis before losing 1-0 to Sunderland at Hillsborough.
Norwich have met Leicester five times in the FA Cup, winning once – in 1913 when their opponents were still known as Leicester Fosse – but losing the last four ties.
Leicester's last visit, for a quarter-final in 1963, brought the all-time record gate to Carrow Road of 43,984. The Canaries went down 2-0 to goals from Mike Stringfellow and Dave Gibson, while Terry Allcock missed a penalty. Leicester went on to reach the final, where they lost 3-1 to Manchester United.
The last FA Cup meeting between the two sides came in the fourth round in 1997, when Martin O'Neill's Leicester beat his former club 2-1 at Filbert Street. Neil Adams scored from a penalty for Mike Walker's men, while Norwich's Matt Jackson and Leicester's Neil Lennon were sent off.
• Full FA Cup fifth round draw:
Millwall or Southampton v Bolton
Sunderland or Middlesbrough v Arsenal or Aston Villa
Norwich v Leicester
Stevenage v Tottenham
Crawley v Stoke
Chelsea v Birmingham
Everton v Blackpool or Sheffield Wednesday
Liverpool v Brighton
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