Henley tweeted about his dilemma Monday afternoon.
In a statement, United said, "We know how important Mr. Henley's clubs are to him, especially this week, and we apologize for the delay in getting them to him. We flew the clubs this afternoon, and they're out for delivery right now."
United is the official airline of the PGA Tour.
This is not the first time United has lost the golf clubs of a professional player before a tournament. Last year, the airline lost Rory McIlroy's golf clubs when he flew into Dublin, Ireland, for the Irish Open. At the time, McIlroy tweeted about his situation:
United saw the tweet, found McIlroy's clubs and delivered them to the golf course before the tournament began.
United offers a Bag VIP program, which allows travelers to have their luggage delivered to its final destination in the United States. However, there is not a program to ensure a specific piece of luggage gets extra attention.
United said the luggage of every passenger is important and one bag is not more important than another.
Henley went pro in 2011 and is ranked 33rd in the FedEx cup standings.