New Zealand Rugby general manager community rugby Steve Lancaster said all three of the domestic competitions would be affected in some way.
"We know there is going to be some disruption, but we won't know exactly what that looks like until we have consulted with our provincial unions," Lancaster said. "Clearly matches in Auckland will be affected under the current deadline, so we will need to look at our options."
Lancaster also noted the ability of all teams to train together and to travel to and from matches would be restricted.
"The health and safety of our people is paramount and will guide our decisions," he said. "Clearly we may need to reschedule a number of matches, so we will consult our affected provincial unions and go from there."
Also in doubt is the travel plans of several teams who were about to depart New Zealand for international competition.
The All Blacks are set to head to Perth on Sunday for their third Bledisloe Cup match against the Wallabies, with NZR chief executive Mark Robinson keeping a watching brief on the situation.
"All our players are currently on a family break until their scheduled departure to Perth," Robinson said. "We will be guided by government travel guidelines and any potential border restrictions in Australia while working closely with SANZAAR and Rugby Australia in coming days to understand what the impact is on our plans."
The Black Caps are due to depart for tours of Bangladesh and Pakistan early next week, while the Kiwi contingent competing at the Paralympic Games could also be affected.
Some of New Zealand's Paralympians are already in Tokyo ahead of the Games' opening on August 24, but not all of the team's 66 athletes, coaches and officials have yet left the country.
The national women's basketball competition is another left scrambling by the lockdown, with eight games scheduled to be played in Auckland for week two of the Sal's NBL. Those games will not be played this weekend, according to competition general manager Justin Nelson.