The Seasiders, who won the trophy for a seventh time last season after beating Boro Rangers 5-1 at the Riverside Stadium, received a bye into the second round.
The second round tie against the North Riding Football League outfit is scheduled to be played by Saturday, 30th November, with a date to be confirmed on whitbytownfc.com in due course.
NORTH RIDING SENIOR CUP SECOND ROUND DRAW
Fishburn Park or Richmond Town vs Boro Rangers
York City vs T.I.B.S Football Club
Great Ayton United vs Whitby Town
Guisborough Town vs Pickering Town
Northallerton Town vs Redcar Athletic
Scarborough Athletic vs Thornaby
Yarm & Eaglescliffe vs Redcar Town
Middlesbrough U21 vs Marske United