The 29-year-old opener was struck by a throw-down from ex-England international Marcus Trescothick.
"We're here to win the Test match, not to see how many bruises we can give. That's not winning Test matches, trust me."
His absence from the playing XI could pose problems to the Australian batting line-up that often witnesses collapses upfront.
"When someone takes a nasty blow no bowler is going to say 'I'm not going to bowl that again because I don't want to hit them again'."
Smith followed up his stunning twin centuries at Edgbaston with a fluent 92 in the first innings of the second Test.
"It's really pleasing to see someone come in on Test debut and really shake up things and live up to the hype."
Sam Curran was able to retain his place in a 12-man squad for the third Test which starts at Headingley on Thursday.
Labuschagne was not part of the playing XI until Sunday morning when Australia's batting genius Steve Smith was ruled out with a mild concussion.
Australia reached 154-6 in their pursuit of the daunting target of 267 on an abrasive surface posing all sorts of problems to the batsmen.
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