City made it through to the fifth round after beating Tottenham 1-0 on Friday night.
The Hatters and the Citizens have met seven times in total in the competition – but this will be the first time since a 1969 third round tie at Maine Road, which City won 1-0.
Perhaps the most famous meeting between two the clubs came in the FA Cup in 1961. Denis Law scored all six goals as City led 6-2 at Kenilworth Road before the game was abandoned. When the time came to replay the game the Hatters ran out 3-1 winners.
The two sides have already met at Kenilworth Road this season in the Premier League when the visitors came from behind to win 2-1.
The tie will be played the midweek of 26th February. Full ticket information and confirmation of the date of the fixture will be confirmed in due course.