Umenyiora, who missed all of last season with a knee injury, left to tend to an "internal matter," according to his agent, Tony Agnone.
The Newark Star Ledger reported Umenyiora left the team's headquarter over frustrations with new defensive coordinator Bill Sheridan. When asked via text if that report was accurate, Agnone responded only by reiterating that it's an "internal matter."
As speculation grew about why Umenyiora left, he released a statement about the situation Monday night.
"I made a mistake by leaving the facility today. I was wrong," Umenyiora said. "I came in here this afternoon and met with coach Coughlin, coach Sheridan and (defensive line) coach (Mike) Waufle and apologized and explained why I left the building; that will remain between us. I have no problem with our defensive coordinator Bill Sheridan or any of our coaches. That's the end of it, as far as I am concerned."
Umenyiora was with the team early Monday morning then left, a Giants source told NFL Network's Jason La Canfora. Team officials made the assumption he had a personal matter to deal with, and the two-time Pro Bowler exchanged texts this afternoon with general manager Jerry Reese to let the team know he was okay, the source said.
It's unclear if Umenyiora will be fined for his absence.
After missing the last two preseason games with a sore foot, middle linebacker Antonio Pierce returned to practice on Monday.
Also missing practice were safety Kenny Phillips (sore knee), cornerback Aaron Ross (hamstring), halfback Danny Ware (ribs), receiver David Tyree (hamstring) and defensive tackle Chris Canty (hamstring).
Backup offensive tackle Guy Whimper, who was filling in for Diehl, had to leave practice with a hip flexor after colliding with halfback Brandon Jacobs. Free agent offensive lineman Andrew Carnahan twisted a knee.
Coughlin did not know the extent of their injuries.
Information from the Associated Press was included in this report.