Manager Buck Showalter said Sunday that he will move the left-hander back this week, from Tuesday to either Friday or Saturday in Washington.
The 23-year-old Britton is 6-4 with a 3.18 ERA over 13 starts.
Showalter says he wants to conserve Britton, who already has thrown 82 innings and has never pitched more than 154 since being drafted in 2006.
Showalter says, "We have X number of innings we want Zach to pitch. We don't want to shut him down in August."
Chris Jakubauskas will start Tuesday in Toronto. The right-hander started for the first time this season against Oakland on Tuesday, throwing five shutout innings.