Smith is still travelling with the squad and is hoping to recover in time for the second Test in Grenada on July 3.
Josh Inglis and Sam Konstas have been confirmed as their replacements, meaning Konstas will open the batting alongside Usman Khawaja whilst Cameron Green could continue at number three.
“Steve needs more time for the wound to heal so we’ll give him another week’s rest and assess his functionality after that," said Cricket Australia chairman of selectors George Bailey in a media release.
“We have made the decision to give Josh (Inglis) and Sam (Konstas) the opportunity to replace Steve and Marnus. We are excited to see them get the chance to further their fledgling Test careers.
“In his only opportunity in Test cricket to date, Josh was outstanding in Sri Lanka, showing great intent and ability to put pressure on the opposition."
Labuschagne's omission appeared all but confirmed shortly after Australia's loss to South Africa in London when head coach Andrew McDonald told reporters that "most players across their journey get dropped at some point in time" in reference to Labuschagne's future.
He has been declared by McDonald to be "a big part of the future", but in his statement Bailey confirmed that series averages in the mid-20s against Sri Lanka, New Zealand and India were not good enough.
“Marnus at his best can be a really important member of this team. He understands his output hasn’t been at the level we, or he, expects.
“We will continue working with him on the areas of his game we feel he needs to rediscover. We continue to value his skill and expect him to work through the challenge positively.”
The first Test between the West Indies and Australia commences at the Kensington Oval in Barbados on Wednesday 25 June.
