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A statement from the Ministry of Health says he is self-isolating with mild symptoms and will return to New Zealand later than planned.
Dr Bloomfield was attending the Assembly with Health Minister Andrew Little, who left Geneva earlier this week.
Both were following all appropriate health precautions, the ministry said.
Prime Minister Jacinda Ardern tested positive for Covid-19 about two weeks ago and missed the government's announcements of the Emissions Reduction Plan and the Budget due to having to isolate.
She is currently on a tour of the United States and has just secured a meeting with President Joe Biden.