Eovaldi, who has impressed thus far with a 2.05 ERA in four outings, likely has two or three more starts this year before the Dodgers move the 21-year-old to the bullpen.
The right-hander's final start will likely come in the middle of a stretch of 24 straight days with games that began on Friday against Colorado.
Mattingly said in order to break up the workload on his starting rotation, he plans to pitch Eovaldi and the callup back-to-back, giving the other starters an extra day of rest.
The team hasn't made any official decisions yet, so Mattingly refused to speculate on who may earn that starting spot. But John Ely, who has appeared in two games with the big league club this season, figures to be the most likely replacement.