Manager Ned Yost and trainer Nick Kenney came to the mound, and Vargas appeared exasperated and angry. Vargas then left the game and was replaced by Joe Blanton.
The injury was officially called "left medial elbow pain." The Royals have an MRI planned for Vargas on Wednesday.
Vargas said he didn't feel a pop in the elbow, just pain that prevented him from throwing any more.
"It didn't feel good," Vargas said. "I'll probably have some more answers tomorrow.
"More than anything, I hated having to walk off the field. Beautiful thing about this team is they respond to adversity."
But the Royals now will have to possibly come up with rotation answers again after having optioned Yordano Ventura to Triple-A Omaha.
Manager Ned Yost said he wouldn't speculate on what roster moves the Royals might have to make.
"This just happened and we need to see what the MRI says," Yost said.
Jeffrey Flanagan is a reporter for MLB.com. Follow him on Twitter at @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.