"She was bleeding pretty good," he added. "It looked like it hit her right in the eye, so hopefully there's no, you know, loss of vision or anything like that... It's not a fun feeling.
"I probably do it way more than I should. It seems just about every week we're hitting somebody and, you know, it's unfortunate.
"It doesn't feel good, it really doesn't. You feel terrible for them. You know exactly how they are feeling, especially when you've got to go over there and apologise."
The American, 28, missed a number of shots afterwards and was described as "shaken" after the incident on the short par-four sixth hole after attempting to go from tee to green in one shot.
"You can yell fore, but it doesn't matter. If you're 150 yards, you're shouting fore, you can hear it. But from 300 yards, even if none of us said fore, she's going to get hit and that's the unfortunate thing," Koepka added.
A Ryder Cup spokesman said: "She was immediately supported by marshals and assessed by the medical team on site.
"She has been taken to the hospital as a precaution but doctors have confirmed the injury is not serious. The spectator does not have a broken nose, contrary to what some media announced."
Koepka and Tony Finau beat Justin Rose and Jon Rahm on the final hole in the opening fourballs match at Le Golf National.