Police on the island of St Lucia said they were holding two people while investigations were continuing.
Roger Pratt, 62, from Warwickshire, died on Friday
Margaret Pratt, his wife, is being treated in hospital after the attack.
A St Lucian police spokesman said Mr Pratt died trying to defend his wife from attackers, but said there was no evidence he had been shot.
He said: "Nobody has been arrested yet but there are some guys in custody."
Neighbours in Moreton Paddox, where the couple lived, spoke of their horror.
Lavinia O'Shaughnessy, said: "I just feel really upset.
"Margaret was very friendly - she'd pick me up at the end of the road to give me a lift into town if she saw me, she was that sort of person.
"I miss her really, and I'm very sorry to hear about Roger."
Mrs Pratt had celebrated her 60th birthday in St Lucia just a few days before they were apparently set upon by attackers, while moored off the Vieux Fort coast on the southern tip of the island.
Rev John Parker, vicar of the Midfosse parishes which includes Moreton Paddox, said prayers for the couple.
"Our hopes and prayers are with the family and particularly Margaret, and we wish her a speedy recovery."