Head coach Tonda Eckert had hoped for a home draw after his side beat Championship rivals Leicester 2-1 after extra time.
However, he will have to settle for a trip to Craven Cottage against a team currently sat 12th in the Premier League.
Fulham beat Stoke City 2-1 in the fourth round on Sunday, with Saints academy graduate Harrison Reed scoring the winner.
Goals from Cyle Larin and James Bree ensured progression to the fifth round in the year Saints are celebrating the 50th anniversary of their FA Cup win in 1976.
Winners of ties in the fifth round will receive £238,500 in prize money. Saints got £127,00 for beating Leicester.
Fifth round fixtures are scheduled to take place on the weekend of Saturday, March 7, when Saints are currently slated to face Norwich.
Confirmation of TV picks and a new date for that game against Norwich at St Mary’s will be communicated by relevant parties in due course.
Saints beat League One side Doncaster Rovers 3-2 in the third round with goals from Cam Bragg, Cam Archer and Kuryu Matsuki.
Full draw:
Fulham vs Southampton
Port Vale or Bristol City vs Sunderland
Newcastle vs Man City
Leeds vs Norwich
Mansfield vs Arsenal
Wolves vs Liverpool
Wrexham vs Chelsea
West Ham vs Macclesfield or Brentford