Their other batsmen have not looked convincing - experienced opener David Warner has totalled just 18 in his four innings - with Smith being the lynch-pin.
"It was really a no-brainer. He felt a bit better on Monday but he's not going to have time enough to tick off everything he needs to do to be able to play".
Britain's sports minister Nigel Adams has condemned England cricket fans who have been booing Australian batsman Steve Smith, calling their behaviour "distasteful" and saying it is time for the jeering to stop.
England too have been without a star player after James Anderson, their all-time leading wicket-taker, broke down early in his spell at Edgbaston with a calf injury that paved the way for Archer's Test bow at Lord's.
Much of the build-up to the match has focused on how Australia are to handle Archer, whose superb second-innings spell saw him take 3-32 in one of the most exciting Test cricket debuts of recent memory.
"It's always a blow, no doubt about that". We've got to have a plan to counter that and I know our boys will.
Coach Justin Langer confirmed the former Aussie skipper's absence after the latter sat out of training sessions on Tuesday.
Smith - who has risen to number two in the world batting rankings - was pictured with his head in his hands and Langer looking glumly at the ground.
Smith did not take part in the final day of play at Lord's with Marnus Labuschagne replacing him in the Australia team under concussion rules.
Collingwood retired from global cricket in 2011 and played 68 Tests, 197 ODIs and 36 T20Is for England.
Smith did not have a neck guard attached to his helmet which many players do now wear following the death of Phil Hughes in 2014.
Smith could return to action in the three-day tour game against Derbyshire from August 29-31, with the fourth Test in a five-match series at Old Trafford beginning on September 4.
- Cathay Pacific says has fired two pilots over Hong Kong protests
- Elton John defends Harry and Meghan's use of private jets
- India condemns Kabul bombing that killed over 60
- U.S. markets sink, sparking fears of recession
- Hong Kong March Was Peaceful 'Because Police Didn't Attack': Protesters
- PM Modi holds telephonic conversation with US president
- Mayor de Blasio says 'justice has been done' after officer fired
- US issues warrant to seize Iranian tanker off Gibraltar
- Italy's prime minister Giuseppe Conte announces his resignation as political crisis deepens
- Jews Disloyal If They Vote Dem