Celtic captain Stephen McManus lifted the cup this season at Hampden
Three Scottish Premier League clubs will have to start next season's domestic campaign two weeks ahead of the rest of the 12 teams.
They will be competing in the Co-operative Insurance Cup at the first-round stage, which begins on 1 August.
It is a knock-on effect from Scotland winning six places in European competition next season.
Qualifying clubs are exempt from the competition until the third round to assist their European challenge.
Normally, SPL clubs, who are not involved in Europe, begin their League Cup campaign at the second-round stage.
The 32 lowest clubs in Scottish football will participate in the first round of the League Cup.
It just means we'll have a competitive game a fortnight earlier than expected
Hamilton Accies secretary Scott Struthers
Newly-promoted St Johnstone will be one of the three SPL teams involved.
The two lowest-placed teams - between Hamilton Accies, St Mirren and Inverness Caledonian Thistle - after this weekend's final round of league fixtures will be the others.
Falkirk, who are currently bottom of the SPL, are excluded as they will be involved in Europe because of their place in the Scottish Cup final.
The Scottish Football League on Wednesday notified the SPL clubs that they could be back in competitive action earlier than expected.
Hamilton, who could be affected if they finish second or third bottom of the SPL, said they are comfortable with the situation.
Accies secretary Scott Struthers told BBC Scotland: "If that's the case, we'll just have to live with it.
"It just means we'll have a competitive game a fortnight earlier than expected."
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