"You get tested sometimes," he said. "Unfortunately, we have to go through it again."
Blum was injured while fielding a ground ball off the bat of Ryan Spilborghs in the second inning.
"He hit it pretty good, had some top spin on it," Blum said.
The ball jumped up and hit him on the end of the finger, but the 13-year veteran figured it was a typical bad hop kind of thing, until he faced Ubaldo Jimenez in the third inning.
"The second curve I swung at, I had absolutely no grip on my hand," he said.
Blum struck out looking in that at-bat, went into the field and tried to throw in the third inning, but there was a shooting pain.
He was lifted by D-backs manager Kirk Gibson for Sean Burroughs shortly thereafter.
"He's definitely out," Gibson said.
Blum will meet with Dr. Don Sheridan on Monday, who will determine how serious the break is and how long he will be out.
"Hopefully it will be a two- to three-week deal and we'll get back out there," Blum said.
The 38-year-old hit .214 (3-for-14) in six games prior to Sunday after being sidelined for the first three-plus months of the season because of right knee surgery.
"I'm getting to know the team physicians around here pretty good, unfortunately," Blum said. "But they took good care of me the first time with my knee, and I know they'll do a good job with the hand."
Anthony Fenech is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.