The police in the Bahamas said on Wednesday that they had arrested an American man in connection with the disappearance of a Michigan woman who fell overboard while boating with her husband last weekend.

Lynette Hooker, 55, of Onsted, Mich., was reported missing by her husband when he arrived at a boat yard in Marsh Harbour early Sunday morning, the police said in a statement at the time.

Her husband told the police that his wife had fallen off their boat, an eight-foot dinghy, during a journey to Elbow Cay in the Abaco Islands that began on Saturday evening, the statement said. He said he had paddled to shore because she fell overboard with the boat keys, causing the engine to shut off, and that he had lost sight of her after she was carried away by strong currents.

On Wednesday evening, the Bahamian police said that a 59-year-old American man had been arrested in Marsh Harbor and was being questioned. The police did not identify the man or respond to inquires, and the United States Coast Guard referred questions back to the Bahamian authorities.

Hours before the arrest, Ms. Hooker’s husband, Brian Hooker, posted an account of her disappearance on social media, saying that “unpredictable seas and high winds” had caused her to fall from their boat.

“Despite desperate attempts to reach her, the winds and currents drove us further apart,” he said. “We continue to search for her and that is my sole focus.”

Messages sent to Mr. Hooker on Facebook on Wednesday night were not returned.

The couple chronicled their adventures on their YouTube channel, “The Sailing Hookers.” Their most recent videos showed them boating, snorkeling and paddleboarding in the Bahamas.