It is the first time Peterhead have reached this stage of the competition since manager Jim McInally took over in 2011.
They have had three loan players – Josh Mulligan, Lyall Cameron and Danny Strachan – from Dundee this season and the last five meetings between the two clubs have all been in the League Cup.
The three other ties chosen for TV coverage are Annan Athletic’s home game against Rangers (February 12, 5.30pm on Premier Sports), Hibernian’s trip to Arbroath (February 13, 12.30pm on BBC Scotland) and Celtic hosting Championship side Raith Rovers (February 13, 4pm on Premier Sports.
Peterhead get TV date as Scottish Cup tie with Dundee to be screened live