The Top League includes All Blacks Brodie Retallick, Sam Whitelock and former internationals Dan Carter, Liam Squire and Matt Todd.
"We sincerely apologise to all rugby fans across Japan for the disappointment," an official statement said.
"The fact that there have been arrests for illegal drug use across multiple teams is not only a Top League problem, but also a major problem shaking the existence of the Japanese rugby world, and it is considered an emergency.
"We have worked together with all the Top League teams to prevent recurrence, including assigning integrity officers to each team, but we have to say that was insufficient.
"We believe that we have betrayed our fans and society, and we need to work diligently to restore trust, and we need to take even more advanced measures.
"Rugby competition consists of five core values: dignity, passion, unity, discipline, and respect. If any one of these is missing, it's not rugby.
"This incident conflicts with most of the core values and in order to become a league worthy of the name of Japan's peak, we will again pursue improvement in each team's integrity before we resume Top League 2020."
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In a statement on their website, the Hino Red Dolphins wrote its "apologies for scandals by our members".
"A member of the Hino Motors Rugby Club (team name: Hino Red Dolphins) was arrested on March 4 for allegedly using illegal drugs.
"We deeply apologise for being arrested for a serious violation of law. In addition, we deeply apologise to the fans who support Hino Red Dolphins on a daily basis, and to the many stakeholders who support us, for causing great inconvenience."
They would "cooperate fully with the police investigation", the club wrote.
Everson is the second New Zealand rugby player to get caught up in a drugs scandal in Japanese rugby in the past year after former New Zealand sevens representative Steven Yates was handed a suspended prison term in September 2019 for possession of cocaine.
Yates' former teammate Ryota Kabashia was handed a similar sentence on the same charge and their club, Toyota Verblitz, suspended rugby operations and withdrew from the Top League for the remainder of the 2019 season.