The announcement comes after a World Rugby meeting which looked at the impact of the Covid-19 pandemic facing the global calendar.
Wales were due to play the All Blacks in Auckland on 4 July and in Wellington on 11 July, followed by a one-off Test against Scotland in Dunedin on 18 July. The Black Ferns vs USA Test, part of a double header in Dunedin, is also affected.
A statement from World Rugby on behalf of rugby's major stakeholders reads:
"Extended travel and quarantine restrictions that apply to numerous countries, and concerns over adequate player preparation time, mean that any sort of cross-border international rugby competition cannot be hosted in July.
"Monitoring of the potential impact on the remaining 2020 international windows continues in collaboration with international rugby stakeholders and the respective authorities.
"All parties, including member unions, international competitions, professional club competitions and International Rugby Players, will be involved in the evaluation of potential contingency options with a view to achieving an aligned calendar for the remainder of the year.
"All decision-making will be entirely contingent on national Government travel, quarantine and health advice and important player welfare and hosting considerations in line with return-to-rugby guidance recently published by World Rugby."
NZR Chief Executive Mark Robinson said: "With so much uncertainty around international travel because of the Covid-19 pandemic, the decision was really taken out of our hands. From a New Zealand point of view, we are taking a pragmatic approach to the international Test programme.
"We are working hard to explore any and every opportunity to play All Blacks Tests as well as Black Ferns Tests this year and watching with keen interest any Government discussions on a possible trans-Tasman bubble with Australia.
"Women's rugby continues to be at the forefront of all our planning. We still have lots of work to do during these uncertain times, but preparation for Rugby World Cup 2021 remains a priority and the Farah Palmer Cup (FPC) is a key part of that," Robinson added.''
"We are working hard with Provincial Unions and the New Zealand Rugby Players' association on the FPC and will have an update on that in due course."