The Carabao Cup second-round draw will take place at 7.20pm on Wednesday, 13 August.
The ties will be picked out live on Sky Sports Football, with the draw hosted by Sky Sports presenter Mark Chapman.
Argyle progressed to this stage with a comeback victory over Queens Park Rangers, winning 3-2, having trailed 2-0 at half-time.
46 teams will participate in Round Two, including the 11 Premier League clubs not participating in European competitions.
This is the final regionalised round of the competition - Argyle will be ball number 15 in the Southern Section of the draw.
Round Two ties will take place in the week commencing 25 August.
The ball numbers are as follows:
1. AFC Bournemouth
2. AFC Wimbledon
3. Brentford
4. Brighton & Hove Albion
5. Bristol City
6. Bromley
7. Cambridge United
8. Cardiff City
9. Charlton Athletic
10. Coventry City
11. Fulham
12. Millwall
13. Norwich City
14. Oxford United
15. PLYMOUTH ARGYLE
16. Reading
17. Southampton
18. Swansea City
19. West Ham United
20. Wolverhampton Wanderers
21. Wycombe Wanderers
22. Cheltenham Town or Exeter City
