"It was very sensitive in the area, but I'm kind of surprised that there's two broken bones in there," Duke said. "Can't change it, just gotta deal with it."
The injury could keep Duke out of the big leagues until mid-May, depending on how quickly he heals and how long it takes him to build his arm strength back up.
It was believed that Duke, who was acquired from the Pirates in an offseason trade, had the inside track on the No. 4 spot in the rotation.
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Along with Duke, Barry Enright, Armando Galarraga and Aaron Heilman were competing for the final two rotation spots.
"We'll have to deal with it," D-backs manager Kirk Gibson said. "We've got other guys, we'll have to figure out what to do. We've got some depth. You never want to lose anybody. He'll still be a factor for us just not from the get go."
GM Kevin Towers said the loss of Duke would not prompt the club to seek pitching help outside the organization.
"That's why you need pitching depth," Towers said. "Unfortunately, it happened to Zach, but I'm glad we have depth in that area to cover ourselves."
Duke was clearly dispirited by the news, but vowed that he would get something productive out of the four weeks he waits for the bones to heal. He plans on working with the team's medical staff on strengthening other areas of his body, such as his shoulder and elbow.
"Like I said, I can't change it so I'll try to find the positive in it," Duke said. "I just have to make sure I'm ready whenever I have the opportunity to go out there and throw again.
One positive is that the bones were not displaced, which means that Duke will not require surgery to have pins put in the hand.
"It's about as good as I could ask for if they're broken," Duke said. "I'm going to shoot for as short a recovery as possible. Obviously the bones will tell me how much time it's going to take. I'm going to be optimistic for sure."
Duke will undergo X-rays each week to determine how the bones are healing.