Warner paid the ultimate price for his drunken antics in Birmingham last month, left out at Trent Bridge after he was suspended and unable to play for a month.
He will leave the Ashes set-up and join the Australia A squad later this week to play a Zimbabwe XI and South Africa A.
Steve Smith won the race for the No.5 position in the Australian batting line-up, even though he was only called into the Ashes squad at the last minute.
The right hander's selection is a reward for his good form in the tour matches and he's been officially included as a squad member for the entire tour along with debutant Ashton Agar.
Smith's strength facing spin bowling also worked in his favour, with the dry pitch conditions set to suit England tweaker Graeme Swann.
He was unbeaten on 38 at the end of the first day with Australia 75-4 in reply to England's 215.
Selectors are keen for Warner to get match practice under his belt so he is prepared for any potential call-up later in the Ashes series.
The 26-year-old could potentially be available for the third Test at Old Trafford starting on August 1.
Coach Darren Lehmann said Warner was bitterly disappointed.
"It's a hard luck story for Davey - he didn't have the opportunity," Lehmann said.
"He's done everything right around the group since his suspension, but we can't pick him without any form in four-day cricket."
Warner's omission from the first Test isn't officially part of the punishment he received for punching England rival Joe Root after a Champions Trophy match in June.
He was suspended for the remainder of the one-day tournament and Australia's opening two Ashes tour lead-up games as well as copping a fine.