Health staff are now contacting the affected families to offer them treatment to lower the chances of infection.
Chief medical health officer Dr. Paul Van Buynder said the exposure of the infants is very concerning.
"They are too young to respond to the vaccine and some will not have received protection in utero from their mothers," he said in a news release.
The visitor was infectious with early measles at the time, the Fraser Health Authority said.
Van Buynder said it is important for people to get vaccinated against the very contagious illness. In extreme cases, measles can cause brain damage, blindness and deafness.
"This comes after a recent death of a child from pertussis, another vaccine preventable disease. It is a timely reminder that not vaccinating children can have consequences for other vulnerable infants."
The health authority said the eastern part of the Fraser Valley tends to have relatively low immunization rates, and the area has seen several clusters of the virus in previous years.
Last month, health officials warned of measles outbreaks in Whistler, Pemberton, Vancouver's North Shore and on Bowen Island.
The most effective protection against the virus is two doses of the vaccine which is free to all those born after 1957.
About 3,000 Canadians with measles die every year.
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