Velez underwent a CT scan and other tests at St. Joseph's Hospital and Medical Center and was expected to remain there overnight.
The switch-hitting Velez likely will be placed on the 15-day disabled list Sunday. Infielder Ryan Rohlinger, batting .310 in 45 games with Triple-A Fresno, is expected to be recalled to replace Velez on the active roster.
Velez was injured when Pat Burrell sliced a 2-2 fastball from Arizona's Ian Kennedy into the visitors' dugout, causing several players to scatter.
As Bochy described it, Velez was sitting atop the bench at the rear of the dugout, but his view was blocked by his teammates who leaned along the front dugout railing. They scrambled to dodge Burrell's foul ball, but Velez couldn't track its flight.
Bochy said that he didn't know exactly where the ball struck Velez.
"But it was a scary moment, because it hit him pretty good," Bochy said.
A handful of players sitting nearby refused to look at the scene as Velez was attended to by team physician Ken Akizuki and other members of the club's athletic training and medical staff. Bochy said that Velez remained conscious but wasn't very responsive until he was taken from the dugout on a stretcher.
Many Giants dressed and left quickly after their 10-4 victory. But Arizona first baseman Adam LaRoche had a clear view of San Francisco's dugout.
"It made me sick," LaRoche said. "It sounded like it hit the back wall, but it hit him right in the head, right in the face -- I don't know where it got him. He went down so fast I couldn't tell who it was. I'll say a prayer for him."
Speaking to reporters, Burrell wore the same pained expression he displayed immediately after lining his foul.
"When I hit it, I figured somebody got hit, but I didn't know who it was," Burrell said. "It's not exactly a contact sport, but it's a dangerous one sometimes."
Bochy acknowledged that Velez's misfortune distracted the team somewhat.
"There's a lot of concern for Eugenio," Bochy said. "There was a lot of praying at times. But guys kept their focus."