Santos was placed on the paternity list on Friday in order to attend the birth of his third child, a boy. He returned to the club on Saturday afternoon and will be active for Sunday's series finale against Baltimore.
The decision to send Laffey to the Minors came down to the left-hander needing more innings as he tries to crack the Blue Jays' starting rotation later this month.
"We know that we need a starter on the 21st [of April], and we have to get Aaron back down to start and stretch out so he be a candidate for that spot," Blue Jays manager John Farrell said.
Because of two off-days in its early schedule, Toronto was able to go with a four-man rotation since right-hander Joel Carreno started against the Indians on April 8, but the club will need a fifth arm on April 21 in Kansas City.
Laffey was recalled to Toronto after the Blue Jays' home-opening series against the Red Sox but hasn't appeared in a game this season.
Evan Crawford, who was recalled from Double-A New Hampshire while Santos was away, will stick with the Blue Jays and pitch out of the bullpen.
"We feel like Evan has a little more matchup ability," Farrell said, "particularly if we get into a left-right-left-right type of situation and his potential effectiveness against right-handers."