Ridgeons League Cup is a home tie against fellow First Division side Team Bury.
The match will be played on Tuesday, January 25, at Greens Meadow.
Town have an early chance to check out opponents they have already beaten 3-0 away in the First Division Cup on Tuesday when Team Bury are the visitors to Stowmarket in the league.
The other three quarter-final ties are: Stanway Rovers v CRC or Brantham Athletic, Walsham-le-Willows v Wroxham or Godmanchester Rovers, Wisbech Town v Great Yarmouth Town or Kirkley & Pakefield.
Stowmarket Town's reward for beating three Premier Division teams to reach the quarter-finals of the