The South Africa pacer was found guilty of a level two International Cricket Council code of conduct offence of "inappropriate and deliberate physical contact with a player" after shoulder-charging Australia captain Steve Smith when he dismissed him in the first innings.
Australia will need their top order to fire against New Zealand's disciplined attack and persist with four specialist bowlers.
England failed to make the inroads into the Australian batting order they needed after gambling on bowling first in the inaugural day-night Ashes Test on Saturday and the hosts reached the second break on 138 for two.
South Africa were 140 for six wickets in their first innings when rain brought an early close to play on the second day of the first test at SuperSport Park on Thursday. Mitchell Johnson had figures of 4 for 51.
Images from Day 4 of the 5th and final Ashes Test between Australia and England at the SCG in Sydney on Sunday
Wade will instead head to New Zealand with Australia's Twenty20 squad for a five-match series starting on Feb. 22 in Christchurch.
Top class left-armers are in short supply and chief selector Rod Marsh joked that he had mulled telephoning Johnson to see whether he might like to come out of retirement.
Uncapped pacemen Joel Paris and Scott Boland will make their international debuts for Australia in the first one-day match against India in Perth on Tuesday.
James Pattinson has been recalled to Australia' starting side for the second Test against New Zealand on Saturday, replacing his injured Victorian team mate Peter Siddle.
South Africa continued their recent dominance of Australia in this format having won 11 of their last 12 ODI meetings dating back to 2016.
Janneman Malan, who was out to the first ball of the match on debut on Saturday, anchored the South African reply, taming his usual swashbuckling style to score 129 not out from 139 balls and lead the home side to victory with nine balls to spare.
Rediff.com has the best sports images from the events in the week gone by snapped right here...
James Pattinson grabbed three wickets to brighten Australia's prospects of a comprehensive victory in the second Test against New Zealand with the hosts reeling at 121 for four by the end of the third day on Monday.
Punjab are lying at the bottom of the table with only one win from six matches, while the in-form Lions are the top of the IPL standings with six wins from seven matches.
Injuries worries to in-form opener David Warner and allrounder Mitch Marsh may affect Australia's plans.
Australian fast bowler Josh Hazlewood received his reward for some fine domestic form on Wednesday when he was included in a pace-heavy 13-man squad for the first two One-Day Internationals against South Africa next month.
In what will be a dress rehearsal of their opening game in the World Cup, an unbeaten Australia take on England in the cricket tri-series final, in Perth on Sunday.
Former Australia cricket captain Steve Waugh and paceman Jason Gillespie have both expressed an interest in succeeding Rodney Marsh as the country's chairman of selectors.
Since an acrimonious series defeat at home to South Africa a year ago, Australia have won nine of their past 13 Tests.
Josh Hazlewood and Brad Haddin set new milestones as Australia, replying to India's first innings score of 408, ended Day 2 in the second Test at the Gabba on 221 for four. Check out the day's days statistical highlights.
Jake Lehmann's strong form could force an awkward decision at the selectors table where his father sits.
In a bid to discourage youngsters from joining the lucrative Indian Premier League (IPL), Cricket Australia is mulling over increasing their contract values, according to a report.
Swing and seam friendly conditions, a lack of truly scary Australian bowlers and New Zealand captain Brendon McCullum's retirement are all themes that will resonate when the first Test gets underway in Wellington on Friday.
Australia's troubled Ashes tour of England continued when they drew with county side Northamptonshire on Sunday.
Kane Richardson gets nod ahead of Josh Hazlewood as replacement
Glenn Maxwell blasted a splendid 83-ball 96 to lift Australia to a three-wicket victory against India that also helped the hosts seal the five-match ODI series 3-0, in Melbourne, on Sunday.
Images from Day One of the first Test between Australia and India at the Adelaide Oval on Tuesday. Australia ended the day on 354-6.
Paceman James Pattinson took five for 27 to fire Australia to a thumping innings and 121-run victory with more than two days to spare in the first Test against West Indies in Hobart on Saturday.
Australia are yet to hit their stride, but that's exactly why the rest should worry, says former Aussie great Allan Border.
IMAGES from Day 4 of the 3rd Test played between South Africa and Australia in Cape Town on Sunday
Unheralded left-arm spinner Steve O'Keefe grabbed a sensational match-haul of 12 wickets as a sloppy India slumped to a humiliating 333-run defeat inside three days in the first Test against Australia in Pune.
Having dismissed England's openers for a combined 17 runs on day four, Hazlewood required just one delivery to make the first breakthrough of the morning.
South Africa's Temba Bavuma was left stranded on 95 not out as they tightened their grip over scandal-hit Australia after reducing the hapless visitors to 110 for six at the close on the second day of the fourth and final Test on Saturday.
Penpix of players in Australia's Ashes squad.
Factbox on the five-Test Ashes series between England and Australia
'He knows what works best for him in the shortest format, T20. It's probably just about finding that balance at international level as well'
? Australia's players feared another backlash from New Zealand fans after a contentious no ball decision went in their favour in the final over of the first day's play of the first Test on Friday.
Dinesh Karthik scored a fighting fifty (58 off 44) but it went as vain as the Lions kept losing wickets at crucial junctures to make a hash of the chase.
India's Rohit Sharma jumped eight spots to enter the top five in the ICC batsman rankings after a stellar showing in the recently concluded series against top-ranked Australia.
India beat Australia by 75 runs in the second Test to level the four-match series at 1-1 after home off-spinner Ravichandran Ashwin took 6-41 on the fourth day in Bengaluru on Tuesday.