Koepka, 28, fired a wayward tee shot on the sixth hole into the crowd during the Ryder Cup opening day on Friday.
The ball struck Corine Remande, 49, in the eye.
Ms Remande is understood to have lost sight in that eye after her eyeball ‘exploded’, while her eye socket was fractured.
And Koepka has issued a statement on instagram regarding the incident.
“I was deeply hurt and saddened by the tragic accident that occurred when a shot I hit off the 6th tee struck Ms. Remande,” the statement read.
“I spoke to her at the time on the golf course and after now learning her condition is worse than first thought, I have made contacted with her/family to offer my sincere and heartfelt sympathy.
“My thoughts remain with Ms. Remande and her family, and I have asked to be kept informed on her condition.”
Ms. Remande is understood to be seeking legal advice following the incident.
She was taken to hospital in Lyon, having been transferred from Paris over the weekend.
“Quite clearly, there is responsibility on the part of the organisers,” said Ms. Remande.
“Officials did not shout any warning as the player’s ball went into the crowd.”
Koepka endured a miserable Ryder Cup as the USA were thrashed by hosts Europe in France.
He won just one of his four matches and tied his singles clash with Paul Casey on Sunday.
During Friday’s incident, the TV commentators noticed Koepka looked “shaken up” by what had happened.
“I hate to report this but Brooks is a little shaken up,” one of Sky Sports’ on-course commentators said.
“A spectator caught the golf ball. It looks to be right above her eye.
“There are fairly worrying moments for one of the fans out here. Hopefully everything is okay.”
Europe captain Thomas Bjorn added: “For me, the whole team I represent and everybody at Ryder Cup Europe, it’s just a terrible thing and something that you don’t want to happen.
“It’s terrible, it’s a freak accident that’s happened, and all our thoughts are with her.”
In a statement a Ryder Cup spokesperson said: “It is distressing to hear that someone might suffer long-term consequences from a ball strike.”
BBC Sport’s golf correspondent Iain Carter said: “Spectating at golf tournaments can be a hazardous business. Top players are not as precise as you might expect and errant tee shots occasionally have nowhere to go other than into packed galleries.
“These misdirected missiles have the speed to do plenty of damage but more often than not injuries are limited to cuts and bruises. Players usually offer a signed glove to the victim, as if that will ease the pain.
“In more serious incidents, injuries can be very unsettling for the players involved. The majority sound a warning cry of “fore” but there are some who appear content to allow fans to be a barrier to prevent their balls from flying into deeper trouble and remain silent in the wake of wayward blows.”