Warner, who was suspended from the warm-up matches for hitting England batsman Joe Root in a Birmingham bar lost his place to Steve Smith, who will be playing as the No.6 batsman. Warner was overlooked due to his lack of match practice.
Warner will depart later this week and link up with Australia A in Zimbabwe and South Africa.
"David has trained hard and been very supportive of the team and his team-mates during the past few weeks, but his preparation for the First Test was not ideal. He is in need of match practice and runs in the longer format and the Australia A games in Zimbabwe and South Africa will provide him with the best possible opportunity," said National Selector John Inverarity.
Warner, however, will continue being a member of the Ashes squad.
"David remains a member of the Ashes Squad and will return to the England at an appropriate time once we're happy he has had adequate preparation in match conditions.
"Steve Smith will stay on with the Ashes squad for the full tour in England. As a consequence of this Aaron Finch will take over the captaincy of Australia A while Alex Doolan has been promoted to vice-captain.
"The NSP (National Selection Panel) also announces that Ashton Agar has become an official member of the Ashes squad for the series," Inverarity said.
Agar, 19, a left-arm spinner made his Test debut after having played just 10 first class matches.