Per Matt Campbell and Rustin Dodd of the Kansas City Star, Duffy was cited by an Overland Park police officer around 8 p.m. local time for driving under the influence.
Per TMZ Sports, Duffy wasn't placed in jail because alleged DUI offenders in Kansas "can be cited and picked up by a friend," according to an Overland Park city official. The report also says Duffy was stopped by police at a Burger King.
Duffy is scheduled to have an appearance in municipal court Sept. 19, according to the report.
The 28-year-old Duffy was placed on the 10-day disabled list Sunday with a sore left elbow. Royals manager Ned Yost said an MRI revealed Duffy had a low-grade pronator strain, and the team was hopeful he would miss only one start, per MLB.com's Jeffrey Flanagan.
In 21 starts this season, Duffy has a 3.78 ERA with 116 strikeouts and 36 walks in 131 innings. He missed more than one month from May 29 through July 4 with a strained oblique.