State police said Thomas Wayne Markle Jr. was visibly intoxicated when he was pulled over at about 1:30 a.m. Friday in Josephine County, in southwestern Oregon.
Authorities said his blood-alcohol content was 0.11 percent, above the legal limit of 0.08 percent.
The 52-year-old from Grants Pass was taken to a detox center.
Meghan Markle, a former actress, married Prince Harry last May. They are expecting their first child.
The duchess is reportedly estranged from her father's family. Thomas Markle Sr. said in a television interview last month he had not heard from her since the wedding.
Thomas Markle Jr. did not appear to have a listed phone number, and it was not clear how to reach him for comment.