Jennifer Wilson, from Antrim, Northern Ireland, was treated by medical staff after being driven away in a golf cart. Woods had earlier apologized and given the 63-year-old an autographed glove.
Wilson was struck just short of the green at the par 5 sixth hole at Carnoustie, where she was standing with her husband.
"We were standing 30 yards short of the green and I said to Jennifer: 'Get your crash helmet on, Tiger's coming,"' Cecil Wilson said. "I could not believe it when Jennifer then got 'clunked,' but he does go off line from time to time. She just sank to her knees and we laid her down flat. She's had two stitches and there was quite a lot of blood. A guy in the crowd said he was a doctor, but to be honest we didn't really need him.
"She was pretty quiet and several people helped to get pieces of paper and napkins to stem the bleeding. She's lying down, but is hoping to go back and see some more golf. We are trying to get Tiger to sign the ball. My wife did him a favor, she headed it back in for him."
Woods went on to par the hole, at which point he was 1 under, five behind leader Sergio Garcia.