The Iran-aligned Houthis control much of northern Yemen, including Sanaa, and are battling a Saudi-led coalition that is trying to restore the internationally recognised government.
Nadia Burch told Reuters that her husband, Danny Lavon Burch, was seized on Saturday after taking his children to school. He had been working in Yemen since the late 1980s, currently with the oil company Safer, said Burch, a Yemeni.
"He has no problems or disputes with anyone, which is why he didnt leave as others did," she said. "I ask for the release of my husband and his safe return to me."
A U.S. State Department official said they were aware and concerned about the report.
The Houthi movement did not respond to a request for comment and the Safer oil company was also not immediately available for comment.
Two of Mr. Burchs colleagues in Sanaa said Houthi forces were responsible, without elaborating. But Nadia Burch said the kidnappers had not contacted her and she was unsure of their identity.
More than 10,000 people have been killed in Yemens civil war. It began in March 2015 when the Houthis advanced on the interim headquarters of President Abd-Rabbu Mansour Hadi in the southern port city of Aden, forcing him to flee the country and seek Saudi help.