"Both Colby and Brett needed another day," Blue Jays manager John Farrell said. "We'll take advantage of tomorrow's off day and hopefully both will be back in the lineup on Tuesday in Tampa."
Lawrie, the club's everyday third baseman, left Friday night's game with tightness in his rib cage.
When Lawrie returns, Adeiny Hechavarria will remain with the Blue Jays and fill in at second and shortstop, Farrell said. Hechavarria made his Major League debut at third in place of Lawrie on Saturday, even though he is a middle infielder.
Rasmus, the center fielder, suffered a strained groin on Friday night. He stayed in the game for a couple innings after he was hurt. Farrell said Rasmus was available to pinch-hit in Sunday's game.
Two other injured Blue Jays took steps toward recovery.
Jason Frasor, who has been out for two weeks with discomfort in his forearm, will start throwing on Monday.
Adam Lind, who is out with tightness in his back, has started to take some dry swings, but there remains no timetable for his recovery, Farrell said.