Worthing United players Matthew Grimstone and Jacob Schilt, both 23, were among the victims of Saturday's crash.
Both players supported Brighton, with the former a member of the club's ground staff. The Sky Bet Championship team will play their second round match at Walsall on Tuesday evening.
Football League chief executive Shaun Harvey said: "This minute's silence will give football fans across the country the opportunity to pay their respects to Matthew, Jacob and all those who lost their lives in this terrible accident.
"On behalf of The Football League our condolences go to everybody at Brighton and Hove Albion, Worthing United and to all those outside of the football family who have been rocked by Saturday's shocking events."