But the minister, who was in the US at the time of McDowell's victory, said she believed it could attract touring golf fans.
"When I was in America last week on a trade mission it really was tremendous to see the focus Northern Ireland was having because of Graeme McDowell's tremendous win last Sunday in the Open," she told the Assembly.
"People were congratulating me simply because I was from Northern Ireland.
"I just think it has tremendous potential. I know that Tourism Ireland are looking at that potential and seeking ways in which they can benefit from it."
She added: "I was incredibly proud of him when I was in the United States of America. It was almost a precursor to my arrival in California that the Northern Ireland Minister for Tourism had arrived just as Graeme McDowell had won the US Open.
"It was a tremendous occasion for him. I have written to him to tell him how much we are proud of him, but also the fact that he has really put Portrush and North Antrim on the map. I had already met with Royal Portrush before his tremendous victory. I hope to meet with them again to see if there's more we can do in relation to golf tourism."
She said she had met the Minister of Environment to discuss the need for golf courses and golf resorts.
Ms Foster also backed a call from the SDLP's Alasdair McDonnell for more direct flights into Northern Ireland to attract overseas visitors.
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