No reason has yet been given for Smith's decision to withdraw and speculation has heightened in Barbados over the sudden move after he played in the final national Super50 trial match this week, BCA's reported.
Smith was due to leave Barbados earlier this week for London enroute to Australia but has remained in Bridgetown after reportedly making two trips to the airport.
The website quoting well placed sources reported that Smith in one instance "dramatically asked airline officials to disembark the aircraft" when it was on the runway at the Grantley Adams International Airport (GAIA).
The BCA said that Smith had informed Perth Scorchers officials through his agent that he would no longer be playing in the Big Bash League this season.
The BBL started Dec 20 and runs until Feb 15.
Perth Scorchers' first match is against Brisbane Heat Sunday.
Reports also suggest that Smith has been included in the West Indies squad for the two-match Twenty20 International series against New Zealand Jan 11 and 15.
Smith has represented Sussex, Deccan Chargers, Mumbai Indians and Barbados at T20 level.
In addition, he also played for New South Wales in the BBL in 2009.