Jamaican police have launched a murder enquiry after announcing that the 58-year-old Briton had been strangled in his hotel room.
There is widespread speculation that Woolmer's death might be connected to a "betting mafia" involved in match-fixing but Donald said he "would be gob-smacked if he was involved in anything to do with match-fixing or corruption."
Woolmer was coach of South Africa from 1994-99, a period in which their late captain Hansie Cronje was implicated in match-fixing, but Donald, close to both men, dismissed a further connection.
"If anyone suggested Bob had anything to do with bookmakers or match-fixing I'd say they were talking rubbish," he said.
"There have been rumours that Bob might have received death threats in the past and there's no doubt fans from Pakistan and India are fanatical," he told Britain's Sun newspaper before the confirmation that Woolmer had been murdered.
"The only possible link I could see to match-fixing is that someone who lost a lot of money misguidedly sought revenge on Bob.
"It would be enormous if he was murdered, just an incredible shock. If foul play was the cause then cricket will be rocked for months and years to come."
Pakistan have been eliminated from the World Cup after their shock defeat by Ireland last weekend but Donald said Woolmer would have been philosophical about the setback.
"Defeats and bad results just didn't affect him in the same way they did some people," he said.
The paceman said Woolmer had been hugely supportive in the aftermath of South Africa's excruciating defeat by Australia in the semi-finals of the 1999 World Cup when Donald was run out off the last ball.
"Bob tried to calm us down. We've only lost a game of cricket,' he kept telling us, and he was right of course.
"Bob was very close to me for the majority of my cricketing career. When his wife rang me to break the news I was ice cold.
"He was extremely professional, extremely soft. He gave his life to cricket and probably paid for it with his life."
