"We've done some of the standard testing protocols, which diagnosed a mild concussion," Price said. "Now it's a matter of checking on him each day, giving him some rest and seeing how he responds on a day-to-day basis."
It was the second concussion of Mesoraco's career. He also sustained one on July 30, 2012, following a home-plate collision that required his being placed on the seven-day disabled list.
Mesoraco is 2-for-8 in three games this spring.
Third baseman Todd Frazier, center fielder Billy Hamilton and second baseman Brandon Phillips all have more minor injuries.
Frazier, who is 1-for-6 in three spring games, has back spasms and expected to miss a "day or two."
"I'll be fine," Frazier said. "I just need some time."
On Thursday vs. the Cubs, Hamilton hurt his right shoulder when hit the wall trying to catch a drive hit by Matt Szczur. It wound up going for a triple.
"It's just sore," said Hamilton, who is 2-for-8 in three games with a home run. "It will be a couple of days and we'll see how it goes from there. Nothing major. If I had to play today, I would be fine. If it were the regular season, it would be no problem."
Phillips, who is 1-for-6 so far in his three games, has a groin injury.
"It just doesn't make sense at this point in time to run them out there," Price said of the players.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.