Early in her pregnancy, Whitney Peak traveled to Rio de Janeiro for her job with Leblon Cachaça, a liquor company based in Brazil. That was in October, before much was known about Zika, a mosquito-borne virus that has spread through South America and that scientists say may be linked to a birth defect and brain damage in babies.

She was scheduled to return to Rio in late January for some Olympics-related marketing projects. But after consulting with colleagues, she canceled the second visit — and now regrets the first.

“It is very scary to know I could have unknowingly put my child at risk,” said Ms. Peak, who is still pregnant. “When the time came for the planned trip, I don’t think there was any question that the risk for me to go was too high.”

With reports of Zika infections on the rise, employees and management at a variety of corporations are grappling with how to handle jobs and projects in affected regions.