Hillman made the announcement after Sunday's practice session. Guillen and the other position players were scheduled to join the workouts on Tuesday.
"We just got really sad news. Jose has lost one of his siblings -- just passed away," Hillman said.
"So he's going to be late. I don't know how late -- maybe a day or two -- but he's going to be taking care of the obvious arrangements."
No details were immediately available, but Hillman believed that Guillen was going from Miami to the Dominican Republic to join family members.
Guillen and Alberto Callaspo are the only two position players on the 40-man roster not yet in camp.
The Royals, on their fourth official day of pitcher-catcher workouts on Sunday, stayed off the practice fields for the second straight day. Overnight rain soaked the complex, and it was again chilly.
Rather than risk pitchers slipping on wet grass during fielding practice, Hillman had them drilling under cover with softer baseballs on the dirt of the batting cages.
"Comebackers with the ragballs is always an event, it changes it up a little bit. They had a competition with it today, and Brian Bannister beat out Kyle Davies in the finale," Hillman said. "It's good for hand-eye coordination, and we wanted them to do some fielding today."
On Monday morning's schedule was batting practice with the Major League pitchers throwing against Minor League batters. If the fields are still too wet, that might be held in the cages, as well.