Both were following all appropriate health precautions, the ministry said.
The World Health Assembly is described as the World Health Organisation's decision-making body, where the WHO's work is reviewed and new tasks assigned.
Bloomfield has led New Zealand's official public health response to the pandemic for more than two years.
Today, the Herald learned he had tested positive for the virus.
At least 1.13 million Kiwis are known to have contracted the virus since the pandemic began.
Bloomfield has been the Ministry of Health's chief since 2018.
Epidemiologist Prof Rod Jackson today said Bloomfield's leadership had been "incredibly important".
As a leader, he had brought a unique set of skills and knowledge which had helped New Zealand keep Covid-19 death rates relatively low.
"He's worked in DHBs, in the ministry, he worked in NGOs," Jackson said.
"We lucked in in a big way. I really mean that. He understands clinical practice. He understands the whole range of groups and relationships in the health services, better than anybody."
Bloomfield is due to step down from the role in July. When he announced his resignation last month he was lauded by Prime Minister Jacinda Ardern as a "true public servant" who worked tirelessly during the Covid-19 pandemic.
"Through his tireless dedication, his focus on people, his calm and considered approach - he has been a true public servant," she posted on social media at the time.
"He has been central to our Covid success as a nation, and he's done it with humour and grace ... When we spoke about his decision to move on, he mentioned that he wanted to spend time with his family, and that's the least we owe him."
In a message to ministry staff the day he announced his resignation he said the director-general role was complex and challenging.
And he said with a once-in-a-century pandemic, the past two years had been especially challenging and intense.
Bloomfield said he had done everything he set out to do when he came into the role before praising the efforts and support of committed and talented people in the ministry and across the wider health system.
Bloomfield said his focus in the remaining months in the role would be to ensure the ministry was well placed to transition into the new health system.
But after a demanding two years, he was also eager for some down time.
"I'm looking forward to taking an extended break and spending time with family before deciding on what I will do next."
Covid-19 Response Minister Chris Hipkins has praised Bloomfield's work as a "calm, informative and reassuring figure" during the pandemic response.
"The amount of pressure he's absorbed, and the level of commitment he's shown over the past two years make that an easy decision to understand," Hipkins wrote on social media.
"We thank you Ashley for all you've done to keep us all safe. Give the man a beer, he's truly earned it!"
Bloomfield qualified in medicine at the University of Auckland in 1990 and spent 2011 at the World Health Organisation in Geneva.
The father of three has routinely described Covid as a "tricky" virus and one that New Zealanders need to be on their guard against.