New Zealand Rugby CEO Mark Robinson said rescheduling the matches had been challenging, particularly having to move the two tests out of Wellington.
"It is particularly disappointing we will not be able to play in Wellington this season and we share the disappointment of fans, the venue and the city, but at short notice following the closure of the travel bubble with Australia it just proved too difficult."
Robinson said organisers had tried hard to retain the games.
"Sky Stadium, Wellington Rugby and WellingtonNZ did everything they could to try and keep the Test in Wellington, but ultimately we needed to play on Saturday 14 August."
He said the All Blacks would be back at Sky Stadium in 2022.
Sky Stadium Chief Executive Shane Harmon said losing the two rugby matches was a huge blow.
"Naturally we are very disappointed, we explored every possible avenue to make these matches happen but it just wasn't meant to be, unfortunately."
Harmon said they made the date of Sunday August 15 available for a game, though NZ Rugby decided August 14 would be the only date that worked for them.
NZ Rugby's preferred option would have clashed with New Zealand's biggest beer festival, Beervana, which is being held in the stadium on August 13 and 14.
He said they were looking to get a full house for the Bledisloe Cup match on August 28.
WellingtonNZ Chief Executive John Allen said the test matches pump between $6 to $8 million dollars into the local economy.
"Tests against Australia are generally at the higher end because fans know an All Blacks v Wallabies match will be a fast-paced competitive event.
"They attract thousands of people from out of town, who make a weekend of it, staying in hotels, shopping and enjoying themselves in our eateries and bars.
Allen said the Argentinian match would have also provided a boost given the premium on international sport.
"Losing both tests is a significant economic blow for Wellington, particularly the hospitality, accommodation and retail sectors that are already facing big Covid challenges. We feel their pain."