The match was scheduled to be played on Saturday as part of the "Blues Footy Fest" event at Eden Park.
Blues CEO Andrew Hore says their priority is the safety and wellbeing of their players, staff and fans.
"We completely understand the situation and we support the directive from the New Zealand Government to reduce risk of any exposure and spread of this virus," Hore said.
"We all need to do our part to protect any spread of Covid-19 and at the current Level-3 Alert means we are unable to proceed with the game."
The match came about after the final game of the 2020 Super season between the two sides at a sold-out Eden Park was also cancelled after Auckland moved to a Alert Level 3.
Hore said finding a replacement pre-season playing opportunity is vital to the Blues preparations for the Super Rugby Aotearoa competition.
"Pre-season fixtures ensure an even playing field, adequate conditioning and preparation for the intensity of the competition. We are exploring all avenues in order to play a pre-season game due to its importance to the overall outcome of the competition and our ability to be a genuine contender."
The Blues will continue to work closely with New Zealand Rugby and the New Zealand Government.