However pregnant women should still keep away out of precaution, he said.
Facing international concern over Zika less than two months ahead of the Olympics, Health Minister Ricardo Barros told journalists that chances of catching the mosquito-carried virus in Rio de Janeiro will be almost zero.
"The statistical forecast is that out of the 500,000 foreigners coming to the Games in Rio, less than one tourist will be infected," he said.
Barros said the figure was extrapolated from studies into the spread of dengue -- a disease transmitted by the same mosquito -- during Brazil's hosting of the football World Cup in 2014, when three out of 1.4 million tourists were infected.
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In an added complication, there is limited, but growing evidence that Zika can be transmitted sexually.
Brazilian officials insist that the Olympics will be safe, because they take place in the southern hemisphere winter when mosquito numbers plummet. In addition, sporting sites will be regularly fumigated.
The Brazilian health ministry says that the Zika outbreak peaked in February with 16,059 cases, while in May the number was 87 per cent down at 2,053.
Last month, 150 scientists signed an appeal to the WHO to ask for moving or delaying the Olympics because of the risks of the still mysterious virus. Barros says Brazil rejects this as "having no scientific basis."
"Brazil is on the front line of aiding and informing the public on this virus," Barros said. "It's not an alarming situation but we have to keep careful watch.