Holders Rangers will kick-off their defence of the Sky Sports Cup against the University of Stirling or St Johnstone.
The first round will feature eight SWPL 2 clubs, with the winners joined by the top-fight sides in round two.
Dundee United face Kilmarnock, Livingston take on East Fife, Boroughmuir Thistle have been drawn at home to Gartcairn and University of Stirling play St Johnstone in round one.
The first-round matches take place on or before September 7.
Last season's runners-up Hibernian are at home to Motherwell, while Hamilton Accies host Glasgow City, Celtic visit Spartans and Hearts play Montrose in the four all top-flight second round games.
Elsewhere, Partick Thistle play Livingston or East Fife, Aberdeen are at home to Dundee Utd or Kilmarnock, Queen's Park are away to Boroughmuir Thistle or Gartcairn, while Rangers play University of Stirling or St Johnstone.
The second round matches take place on or before October 5.