"It was a tough decision," manager Ned Yost said. "You wait until the end to make sure something else [such as an injury] doesn't happen."
After a rough start this spring, Ohlendorf, 33, threw six straight scoreless innings.
"He threw the ball well," Yost said. "He did a nice job. Good breaking ball.
"You can only take 25 guys on your team. He's definitely a fit over the course of a year. But starting the year out, not right now. The numbers just don't match up. I wish they could. Could he have helped us? Yeah."
Ohlendorf has gone 25-34 with a 4.84 ERA in 145 appearances in the Major Leagues.
Flynn had a terrific spring last year and probably could have made the team had he not had options left and had the Royals not needed to keep Ryan Madson on the roster. Flynn's season then was cut short when he sustained a torn lat muscle in his first outing at Triple-A.
"He needs to pitch," Yost said. "He pitched two-thirds of an inning last year. He needs to build strength in that shoulder. He's going to help us this year.
"He came out the first couple of outings and he was just like last year -- dominant. But the more you throw, the more fatigue sets in. It's just building up into pitching shape for him."
Alexander did not give up a run in eight appearances this spring. He yielded four hits and struck out 10 in eight innings.
"Alexander was one of the guys who came in here from last year to this year with great improvement," Yost said.
The Royals reassigned catcher Parker Morin and infielders Orlando Calixte and Dusty Coleman to Minor League camp. The Royals have 37 players remaining in Major League camp.
Jeffrey Flanagan is a reporter for MLB.com. Follow him on Twitter at @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.