Winners of the cup in 1913 and 1957, they will play John McGlynn’s side at The Falkirk Stadium.
The Stark’s Park side sit in third place in the Championship after 10 matches, sitting on 18 points.
All three previous matches between the two teams ended in a draw.
Stenhousemuir have been drawn at home against League 1 side Airdrieonains.
Stephen Swift’s side beat Highland League side Huntly 4-1 on Saturday to get to this stage of the competition.
Captain Sean Crighton will face his ex-club, who he also captained over a four year spell at the Penny Cars Stadium.
Ties will be played on the weekend of Saturday, November 27.