A date for Blues' game will be confirmed in due course, but it needs to be played before 7pm on Saturday 14 December 2019, unless mutually agreed otherwise.BCFC.
Shrewsbury host Sunderland in their second round tie next Friday 15 November.
Sunderland Under-18s are currently bottom of the Under-18 Premier League, having lost all nine of their league games so far.
Meanwhile, Shrewsbury who play in the EFL Youth Alliance North West Division, are presently in eighth place in the 14-team division. They beat Port Vale 1-0 in their first round tie.
A date for Blues' game against the winners will be confirmed in due course, but it needs to be played before 7pm on Saturday 14 December 2019, unless mutually agreed otherwise.
The full FA Youth Cup third round draw is as follows:
1 Manchester City v Swansea City
2 Shrewsbury Town or Sunderland v Birmingham City
3 Cardiff City v Ipswich Town or Exeter City
4 Cheltenham Town or Portsmouth v Arsenal
5 Stevenage or Brentwood Town v Aston Villa or Peterborough United
6 Carlisle United or Bradford City v Stoke City
7 Manchester United v Lincoln City or Wrexham
8 Wigan Athletic v Croydon or Bath City
9 Preston North End v Bristol City
10 Sheffield United v Hanworth Villa or AFC Wimbledon
11 Fulham v South Shields or Hartlepool United
12 Norwich City v Newcastle United
13 Bristol Rovers v Southampton
14 Luton Town v Sheffield Wednesday
15 Blackburn Rovers v Uxbridge or Newport County
16 Chelsea v Huddersfield Town
17 Mansfield Town v Queens Park Rangers or Rotherham United
18 Reading v Crystal Palace
19 Wolverhampton Wanderers v Nottingham Forest
20 Fleetwood Town v Watford
21 Brighton & Hove Albion v Leicester City
22 Middlesbrough v Dulwich Hamlet or Forest Green Rovers
23 Tottenham Hotspur v Liverpool
24 Leeds United v Hull City
25 Burton Albion or Bolton Wanderers v Millwall
26 Crewe Alexandra or Grimsby Town v Barnsley
27 Colchester United or Oxford United v Ware or Maidenhead United
28 AFC Bournemouth v Barnet or Cambridge United
29 Curzon Ashton or Oldham Athletic v Burnley
30 West Ham United v Charlton Athletic
31 Derby County v Everton
32 West Bromwich Albion v Scunthorpe United or Morpeth Town