Woolmer, a former South Africa coach, was 58 years old and his death came just a day after Pakistan, the 1992 world champions, were dumped out of the World Cup by Ireland's part-timers.
P.J. Mir, Pakistan team media manager, told reporters at the Kingston University Hospital, where Woolmer died: "The whole Pakistan team is shocked and saddened that Bob Woolmer has passed away.
"The Pakistan Cricket Board (PCB) extends its deepest sympathy to his family. The chairman of the PCB has been informed and he has been in touch with Bob's wife Jill to offer all the support she needs.
"In accordance with Jamaican law, an autopsy will take place to determine the cause of death."
Woolmer was last seen in public when he addressed the post-match media conference at the Sabina Park ground where Pakistan had been humbled by three wickets by Ireland.
Ironically, he talked of the stresses of the coaching job.
"Doing it internationally, it takes a toll on you - the endless travelling and the non-stop living out of hotels."
Late Saturday, he had told AFP of his devastation at the defeat which caused shockwaves throughout the game.
"I am deeply hurt and cannot tell you how it is going to affect me," Woolmer told AFP, saying he would answer more questions on email later in the week.
Pakistan skipper Inzamam-ul-Haq told AFP: "I am shocked and badly hurt. We have lost a good coach and a good person."
There had been huge pressure on Woolmer going into the tournament.
His team forfeited a Test match against England in August 2006 in a row over ball-tampering before two of his best fast bowlers Shoaib Akhtar and Mohammad Asif were caught up in a doping scandal.
Woolmer, who took charge of the Pakistan team in 2004, was seen late on Saturday night, but officials raised the alarm after not seeing him early on Sunday.
When they went to his hotel room, they saw he was unconscious.
In his playing career, Woolmer appeared for Kent in the English county championship and played 19 Tests for England.
He has also coached the South African national team.
Fate brought him to Pakistan in 2004 as coach, regarded the country's hottest post which had seen five changes since 1999 until his arrival.
He forged a strong relationship with captain Inzamam-ul-Haq and saw to it that the skilful cricketers always remained strong in basics.
Born in the Indian city of Kanpur in 1948, Woolmer missed the inaugural World Cup in 1975 due to injury.
His playing career ended prematurely as he first joined Kerry Packer World Series Cricket and then went on rebel tours to South Africa in 1980s.
He steadily developed into a renowned coach, and was credited with pioneering the use of computers in cricket.
Goolam Raja, the South African team manager at the World Cup, said people in the game had the utmost respect for Woolmer.
"I was very close to him, and I had the greatest respect for him as a man and a coach," said Raja.
"I had the highest regard for him and he made a huge difference to South African cricket. Our thoughts and prayers are with his family."
Pakistan fast bowler Shoaib Akhtar said he was "in shock."
"It is a huge tragedy. We are not ready to believe this has happened," Shoaib said.
"I am completely shattered."
Akthar was pulled out of the tournament hours before Pakistan's departure for the Caribbean on fitness grounds.
He had recently patched up relations with Woolmer after an "altercation" during Pakistan's tour of South Africa, which the paceman said was due to the coach believing he had feigned an injury.
"He was a very dear man, he was a great leader and it's an unbelievable tragedy," he said.
Pakistani president Pervez Musharraf and prime minister Shaukat Aziz both sent messages of condolence to Woolmer's family.
"President Pervez Musharraf and Prime Minister Shaukat Aziz have expressed heartfelt condolences over the tragic death of Pakistan Cricket Team Coach Bob Woolmer on Sunday," a statement said.
"In their separate messages, they said that Bob Woolmer had promoted the cause and game of cricket in Pakistan with dedication and single mindedness," it added.
"In their messages to his family they said Bob Woolmer's services to the game will be long remembered by cricket fans."
Pakistan face Zimbabwe on Wednesday in their final World Cup group match.
"The Pakistan team will continue its participation in the tournament. We are due to play Zimbabwe and we will play that match," Mir told AFP.