Morneau, who has been bothered by a sore left wrist, is scheduled to meet with local hand specialist Thomas Varecka on Monday's off-day.
"He's had that thing and he's going to see Dr. Varecka -- our hand guy -- and he wants to check all the information out there," said Twins manager Ron Gardenhire. "So it doesn't make any sense for me to put him out there until Dr. Varecka sees him."
Morneau has also been bothered by a pinched nerve in his neck and left shoulder, and he is hitting just .225 with a .281 on-base percentage and .338 slugging percentage this year.
"His results haven't been very good, and that's because he's swinging one handed," Gardenhire said. "So if we can let these doctors see him and then get him out there, it'll make all of us feel a lot better."