"(The tumor) is almost 100 percent curable," said team physician Michael Lee said on the team's Web site.
The disease was discovered Feb. 6 during a routine physical examination.
Dr. Mark Baldree and a colleague discovered a firm nodule on Davis's throat and an ultrasound and a biopsy followed.
They felt there was a 75-85 percent chance it was a tumor.
"It was not a big surprise," Davis said when speaking about a phone call from another team physician, Dr. Roger McCoy, on Wednesday. "I'm not going through this alone. I believe the whole team is pulling for me, as I would for them. It's just something that I have to fight through."
Davis, 32, plans to start against Cincinnati April 3 and the Los Angeles Dodgers April 8 before undergoing surgery to remove the mass April 10.
Celebrity Families of 2014 [PHOTOS]