Koch one of four sons who inherited the Koch family's Wichita-based business empire but later sold his share to his brothers -- pleaded innocent earlier this week to charges of domestic assault and battery and threatening to commit murder.
Police arrested Koch, 60, at his Cape Cod home after he allegedly had been arguing with his wife and son.
Barnstable, Mass., police were summoned late Monday to Koch's estate by Angela Koch, who told officers her husband punched her in the stomach.
She also told police that Bill Koch threatened "to beat his whole family to death with his belt," Barnstable Deputy Police Chief Michael Martin said Wednesday.
Angela Koch's restraining order against Bill Koch requires him to live in the estate's guest house or beach house while Angela Koch stays in the main house, The Wichita Eagle reported Thursday. He also cannot be at the couple's West Palm Beach, Fla., home when she is there.
Also, none of the agreement can be the basis for a subsequent divorce or custody action. It stipulates, too, that Koch cannot drink alcohol for 24 hours before visiting his children, who will be accompanied by their nannies, court records show.
The order runs until Sept. 11. It requires Bill Koch to stay 100 yards from his wife, but it makes exceptions for the couple to attend social events and therapy together.
Through his spokesman, Koch said Wednesday: "Every marriage has its problems, and my marriage to Angela is no exception. I love my wife and have every confidence that with the help of competent professionals we will be able to work out our problems and enjoy a long, happy marriage."
"Angela has been a wonderful wife and mother and has brought me much happiness. Since this is a highly personal matter, I will have no further comment and hope that the media will respect our privacy during these difficult times," he said in a statement.
Angela Koch and the family's children did not require medical attention, Koch spokesman Brad Goldstein said.
After his innocent pleas, the multimillionaire was released on his own recognizance.
He will next appear in Barnstable District Court Sept. 18.
Koch is also known as the yachtsman who won the 1992 America's Cup. He owns the Nauticus Marina in Osterville, Mass.
He has also made headlines for his role in a long-running legal feud with his brothers Charles and David, who run Koch Industries, one of the world's largest privately held companies.
Bill Koch's personal life also was in the spotlight in 1995, when he was in a Boston court trying to evict ex-lover Catherine de Castelbajac from his $2.5 million Boston condominium.
Bill Koch now resides in West Palm Beach, Fla., but spends summers on Cape Cod and makes trips to Wichita, Kan. According to Forbes magazine, his worth last year was $650 million.