Warner was stood down in the wake of the boozy bar-room incident last month and subsequently omitted for the first Test in Nottingham, which Australia lost by 14 runs.
He was to board a plane later on Tuesday to join the Australia A team for a tour of Zimbabwe and South Africa where he would have "adequate preparation" in match conditions, selector John Inverarity said last week.
"It defies belief David Warner is about to leave the Ashes tour for an Australia A tour of Africa," former Australia skipper Border said in his column in Sydney's Daily Telegraph.
"I get the thinking, send him to South Africa and Zimbabwe to find form and bring him back later in the series, but I strongly disagree with it.
"Unless Jimmy Anderson bobs up in the Zimbabwe side, Warner scoring runs won't count for anything," Border added, referring to the England seamer, who took 10 wickets in a match-winning performance at Trent Bridge.
"He would be far better served facing (Australia paceman) James Pattinson in the nets. The standard of bowling he will face in Africa and the conditions will be chalk and cheese to the challenges that await him in England."
Australia's top order struggled in both innings in the first Test, sparking demands from local media to bring the hard-hitting 26-year-old back for the second match, which starts at Lord's on Thursday.
Warner told reporters on Monday that he knew he was on thin ice, but had not been placed under any off-field restrictions by new coach Darren Lehmann.
"(Lehmann) just said to go out there and score runs and be myself," Warner was quoted by Fairfax Media as saying.
"Just get that X-factor back that I can have for this team so hopefully I can score some runs.
"Definitely still enjoy myself off the field. There's no bans, there's no curfews, no nothing. The mistakes, I've learned, I've become more mature off the field as well."