The tie will be played at the Etihad Stadium over the weekend of 24-27 January with the exact date confirmed in the coming days.
City and Fulham haven't met in the FA Cup for 106 years - the last being in 1914 at Hyde Road.
The teams have only ever played each other three times in the FA Cup - the first was a 1-1 draw at Hyde Road, with the Cottagers winning the replay 3-1.
The 1914 tie saw City triumph 2-0.
The West London side, managed by Scott Parker, beat Aston Villa 2-1 in the FA Cup third round on Saturday.
They currently sit fifth in the Championship, 10 points behind joint-leaders Leeds United and West Brom and of their 12 league games on the road this season, they have won four, drawn four and lost four.
Bristol City/Shrewsbury v Liverpool
Portsmouth v Barnsley
Rochdale/Newcastle v Oxford United
City v Fulham
Bristol Rovers/Coventry v Birmingham
Burnley v Norwich
West Ham v West Brom
Millwall v Sheff United
Brentford v Leicester
Northampton v Derby County
Bournemouth v Arsenal/Leeds
QPR v Sheff Wed
Southampton v Middlesbrough/Tottenham
Hull v Chelsea
Watford/Tranmere v Wolves/Man United
The ties will be played between 24 and 27 January.
Ticket details will be released in due course.