Schilling suffered the injury when he was hit in the hand twice in Friday's start at San Diego. He remained in the game after being hit by a comebacker by Ramon Vazquez in the first inning, but left the contest when he was struck on the back of the hand by a line drive by Sean Burroughs in the seventh.
An MRI Tuesday revealed Schilling sustained a hairline fracture of the third metacarpal and a chip off the fourth metacarpal.
"It is what it is, you have to accept it, deal with it, and do whatever you can on a daily basis to get better," said Schilling, who was on the disabled list earlier this season when he underwent an appendectomy.
The team's official Web site reported that head athletic trainer Paul Lessard declined to speculate on when Schilling, who is wearing a removable splint, would be able to return to action.
"All I know is Doc Sheridan said to keep that immobile for three weeks so we'll do that," he said. "We can still do the shoulder work and the leg work and all that fun stuff to keep in condition, so at the end of that timeframe he'll be able to move along better than starting from Point A."
"I can't really tell you exactly when we can expect to see him back on the field," said Manager Bob Brenly. "Optimistically, maybe a little before the (All-Star) break. Pessimistically, a little after."
Losing Schilling is another blow for the two-time defending National League West champion Diamondbacks, who already are without reigning four-time Cy Young Award winner Randy Johnson. He underwent arthroscopic surgery on his left knee on May 1, and is not expected back before the end of June.
"People don't realize the extent of the surgical procedure he had," Lessard told the Web site. "There's sections of his knee right now that are bone on bone, so you're going to get some swelling from time to time. The problem is when you get some swelling you're going to fall back a little bit strength-wise. I don't think he'll be ready in three weeks."
The five-time All-Star is 4-3 with a 3.04 ERA this season. He has surrendered 53 hits and struck out 82 in 71 innings.
Arizona (27-31) is in fourth place in the West, 8 1/2 games behind division-leading San Francisco.
"I don't care what time of the year, 9 1/2 games is 9 1/2 games," Schilling said before Tuesday's 2-1 win over the Chicago White Sox. "I think we'll know rather quickly in the next couple weeks how legitimate our chances of getting back into it are."
Brenly remains hopeful.
"I've seen a lot of teams come back from huge deficits a lot later in the season than we are right now," Brenly said. "I still believe that once we get all of our pieces back together, if we can just stay within shouting distance, we've got a good run left in us."