The SAFA president confirmed the date in an interview with SABC on Friday, revealing that the association opted against making their preliminary squad public.
SAFA had already submitted a provisional list of between 35 and 55 players to FIFA before the May 13 deadline. However, the decision was taken to keep that list confidential, with the focus now on unveiling the final selection once the domestic club season concludes.
Head coach Hugo Broos is expected to name a squad of between 23 and 26 players for the tournament.
South Africa will kick off their World Cup campaign against Mexico on June 11 at the iconic Estadio Azteca.
In preparation, Broos' squad will hold a pre-tournament training camp in Pachuca, Mexico, allowing players to adjust to the high altitude conditions similar to Mexico City, which sits over 2,200 metres above sea level.
Bafana will then travel to Atlanta for their second Group A fixture against Czechia on June 18, before returning to Mexico to face South Korea in their final group match on June 25 at the BBVA Stadium.