David Clark's departure, which also followed criticism for his personal breaches of strict lockdown rules earlier in the year, comes as New Zealand heads into a September general election.
"It has become increasingly clear to me that my continuation in the role is distracting from the government's overall response to COVID-19 and the global pandemic," Clark, who was criticised for taking his family on a beach trip and driving to a mountain biking track, said.
Prime Minister Jacinda Ardern, who had earlier refused calls to sack Clark, citing his critical role in the country's response to the pandemic, said she agreed with his decision.
Three years after becoming the world's youngest female leader, Ardern remains popular, lauded for her compassionate response to last year's Christchurch shooting and swift handling of the coronavirus crisis.
But blunders by her ministers have drawn claims from the opposition there is a lack of talent in her cabinet, a potentially damaging charge ahead of the September election.
Ardern's popularity skyrocketed early in the pandemic as she took decisive action limits its spread, imposing one of the world's toughest lockdowns. But opinion polls released last week show the conservative National Party has managed to trim some of Labour's lead.
"She has no confidence in anyone else not to drop the ball," National Party leader Todd Muller said.
Grant Duncan, an associate professor of politics at Auckland's Massey University said the opposition had been granted an opportunity to "talk of the government's failure to deliver and incompetence." Clark's resignation would help dampen that rhetoric, he added.
Ardern declared in early June that New Zealand had eliminated coronavirus, although she warned there would almost certainly be new cases, as she lifted social distancing restrictions.
Just days later it was revealed that two women who arrived from Britain who were allowed to leave quarantine early on compassionate grounds later tested positive for the virus.
The country still has no known cases of community transmission, but there are 18 active cases at the border through returning New Zealanders.
Ardern appointed Education Minister Chris Hipkins as interim health minister until the September election. It is the second time in 18 months Arden has reshuffled her cabinet, replacing her housing minister last year after he came under fire for the failure of the government's flagship public housing project.
