Morrow suffered a contusion on his right shin after being hit by a line drive off the bat of Wilson Betemit during the seventh inning of Wednesday's game against the Orioles.
The right-hander avoided a major injury but will still have to get through his bullpen session on Sunday without any issues before he is cleared to start Wednesday in Chicago.
"Knowing Brandon, he's going to do everything within his capability to be ready to go once Sunday's bullpen and Wednesday's turn comes around," manager John Farrell said.
The Blue Jays anticipate Morrow will be ready for his next outing, but they are still taking a precautionary approach. He will go through treatment in each of the next two days while also having a light catch to keep his arm active.
The club had the luxury of two off-days in a five-day span, which means Morrow is already scheduled for extra rest in between outings. That added time should be enough for Morrow to make his regular turn in the rotation.
"We would have options to do that, but at this point we haven't needed to address that," Farrell said when asked about possibly pushing Morrow's next start back even further. "As we get through the weekend, we'll get a better read if additional days are needed."
The 27-year-old Morrow arguably has been the Blue Jays' best pitcher this season. He is currently 6-3 with a 3.28 ERA while striking out 62 in 68 2/3 innings as the No. 2 pitcher in the rotation behind left-hander Ricky Romero.