The decision to withdraw Edwards, a former captain, was made by the Barbados Cricket Association (BCA) on Saturday.
BCA said there will be no replacement for Edwards who was due to return home late Sunday.
Barbados defeated Trinidad and Tobago by 28 runs in their opening match Sunday, spurred on by a maiden century from Jonathan Carter.
Edwards, 29, a current West Indies Test and One-Day player, was replaced as the Barbados captain for both the NAGICO tournament and the forthcoming first-class four-day championship of which Barbados are the title holders.
Batting all-rounder Kevin Stoute is leading the side in the NAGICO tournament, while Test opener Kraigg Brathwaite will be at the helm for the four-day championship, which is slated to start February 28