North Korean state TV news announced a woman named Ri Sol Ju is Un's wife. The woman has been seen beside the 20-something leader in recent weeks.
State Department spokesperson Victoria Nuland said the U.S. "would always wish any kind of newlyweds well as they embark" - although it's not clear when the couple got married.
The U.S. and North Korea do not have diplomatic relations, and Nuland said: "I don't think we were invited to the wedding."
She added that the U.S. was more concerned about North Korea's people and urged the leadership to open up the country.
The Associated Press contributed to this report.