The tie will be played at Etihad Stadium over the weekend of the 3/6 January.
The draw took place at the Etihad Stadium Legends’ Lounge, with former City favourite Micah Richards and Arsenal legend Tony Adams drawing the balls.
City and Vale have only met once before in the FA Cup, with the Blues winning 2-1 at Vale Park in 1991.
The teams have met 23 times in total, with City winning 18 and losing four.
The last meeting was in 1999.
Vale won three successive meetings between 1996 and 1998, including successive wins at Maine Road.
The League Two side, currently ninth in the table, are managed by former Macclesfield Town legend John Askey.
🏆 | Well then Valiants...
— Port Vale FC (@OfficialPVFC) December 2, 2019
Looks like we’re off to the Etihad! 🤩
See you soon @ManCity!#PVFC pic.twitter.com/4zcOconcPp
Full draw:
Leicester City v Wigan Athletic
QPR v Swansea City
Fulham v Aston Villa
Chelsea v Nottingham Forest
Wolves v Manchester United
Charlton Athletic v West Brom
Rochdale or Boston United v Newcastle United
Cardiff City v Forest Green Rovers or Carlisle United
Oxford United v Exeter City or Hartlepool United
Sheffield United v AFC Fylde
Southampton v Huddersfield Town
Liverpool v Everton
Bristol City v Shrewsbury Town
Bournemouth v Luton Town
Brighton v Sheffield Wednesday
Bristol Rovers or Plymouth Argyle v Coventry City or Ipswich Town
Eastleigh or Crewe Alexandra v Barnsley
Manchester City v Port Vale
Middlesbrough v Tottenham
Reading v Blackpool
Watford v Tranmere Rovers
Preston v Norwich City
Millwall v Newport County
Crystal Palace v Derby County
Solihull Moors or Rotherham United v Hull City
Brentford v Stoke City
Fleetwood Town v Portsmouth
Arsenal v Leeds United
Gillingham v West Ham United
Burton Albion v Northampton Town
Burnley v Peterborough United
Birmingham City v Blackburn Rovers