"It's probably going to be in the vicinity of six weeks," Yost said. "He could heal faster, but we'll see. It's not a hard line. It could be four weeks. Somewhere between 4-6 weeks but leaning toward six weeks.
"He won't do anything for 7-10 days, and then he'll start functioning again."
Dyson suffered the injury in the Cactus League opener on Wednesday while swinging in his first at-bat. He grounded out and ran somewhat gingerly to first base. But Dyson said he tweaked it the day before.
Dyson had an MRI late Wednesday, after the game.
"I just got to think positive," Dyson said. "I can't stay mad about what happened. Just rehab and stay positive."
As for his return, Dyson said, "It's whenever I'm feeling better. Anyone can throw a timetable out there. It could be quicker. It could be longer."
Center fielder Lorenzo Cain, a close friend of Dyson's who lockers next to him, said it was a tough break.
"It definitely [stinks]," Cain said. "I know how hard he worked, and this was going to be his shot. It's going to be tough, but at the same time he's a very strong-mind person. Hopefully he'll heal up fast.
"We'll be ready to welcome him back when he's ready."
Cain knows how painful oblique injuries are.
"Mostly you rest as much as possible and not do anything to reaggravate it," Cain said. "It's a tough one to come back from. You can't run or even laugh with it."
Dyson's absence will provide an opportunity for Paulo Orlando, among others. But Orlando, who likely would have platooned with Dyson to start the season, will get the first shot to replace him.
"I am looking for someone to win the job," Yost said. "I'm not looking for a platoon."
Yost was impressed with Orlando's rookie season -- Orlando, 30, had a .444 slugging percentage with six triples, seven homers, 14 doubles in 241 at-bats.
"It's taken him a while," Yost said. "Being from Brazil, he's a real late bloomer. He really developed his game in the last couple of years. I was just impressed with his ability to do something to help you win. He's always doing something every day to help you.
"He can play center, right. He can run. He can throw. He can hit. He can hit with power."
Orlando is ready to step in, even if it's just temporary.
"I have to be ready for the role," Orlando said. "Hopefully I can help the Royals."
Yost said, however, that several other players will get a look for the job, including Bubba Starling, Reymond Fuentes, Jose Martinez, Travis Snider and Brett Eibner.