Officers are treating the incident as a robbery which went wrong. It is believed that someone entered their cottage while the couple were asleep.
Police officers are reported to have combed dense shrubbery around the resort.
Mr Mullany was taken to Holberton Hospital, where he is in the intensive care unit.
Police on the island said on Sunday: "An investigation has been launched into the events which led to the death of a British woman in her hotel room this morning.
"Shortly after 5am this morning officers from the Bolans Police station responding to a call, arrived at Cocos Hotel and Restaurant in the Valley Church area, the scene of a murder."
Royal Antiguan Police commissioner Gary Nelson said: "I can tell you for sure they went to bed, and one of the two doors was forced open."
A spokeswoman for Cocos Hotel Antigua, a popular getaway for newly-weds, said they were co-operating closely the police investigation.
A bedroom at the hotel where the couple were staying
She said: "Our thoughts are with the families of the couple concerned."
Its website bills the hotel near Valley Church as an "exclusive resort for those looking to escape to paradise", located between two white sand beaches.
The hillside hotel has 19 cottages, set in expansive gardens overlooking the beaches, which cost up to £330 a night.
Police said reports indicated that the couple were shot "when an intruder or intruders apparently broke into their cottage at the hotel and confronted them".
They said several shots were fired and Dr Mullany was "killed on the spot," while her husband also suffered a gunshot wound.
The couple married on 12 July and arrived in Antigua two days later for a two-week stay at the hotel.
The couple's family released a statement through South Wales Police, and asked the media to respect their privacy.
They said: "We are deeply shocked and devastated at the recent events in Antigua and are struggling to comprehend what has happened to Ben and Catherine."
Dr Mullany's parents are preparing to fly to the Caribbean on Tuesday morning.
Janet Davies, a guest at the wedding, said she could not believe what had happened to the couple.
"My feelings are one of absolute shock and horror. I can't help feeling that the world should not lose two such nice young people," she said.
Dr Mullany was planning to become a GP, and her husband is a physiotherapist.
Pontardawe minister, the Rev Gareth Morgan Jones, said: "She was a very friendly person carving an excellent career for herself in the medical profession, and very well respected by everyone."
An Antiguan police spokesman said officers from the forensic identification and homicide units were gathering evidence and several statements had been recorded and a number of people were being questioned.
Police said it was the 10th homicide on the island this year.
Harold Lovell, Antigua's minister of tourism and civil aviation, said: "Our thoughts and deepest sympathies are with the families of the victims of this incident at this very difficult time.
"I have full confidence in the Royal Police Force of Antigua and Barbuda who are conducting an extensive investigation.
"This isolated incident has deeply shocked our community and we wish to reassure visitors that Antigua and Barbuda is a safe destination."
South Wales Police said two family liaison officers were supporting the families and relaying information to them from the Antiguan authorities and the Foreign and Commonwealth Office.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.