McGregor, 52, was working for Scotland's Alastair Forsyth at the tournament when he collapsed on the ninth hole
"It is with great sadness and deep regret that we report the untimely passing of caddie Iain McGregor during play on the final day of the Madeira Open," the Tour said.
The tournament was halted but resumed after consultation with the players and caddies involved.
"A minute's silence has taken place at the clubhouse and play resumed at 1800 local time," the Tour said.
Forsyth described himself as feeling numb.
"Everybody is in shock," he said. "To see that happen to someone in front of your eyes - I don't know how or when you get over that.
"We spoke to (PGA Tour chief) George O'Grady on the phone before taking the decision to play on because we felt that was what Mac would have wanted.
"He was far too young for this to happen. He was the life and soul of the caddies' lounge and a nice guy who will be sorely missed. I'm absolutely numb."
England's Daniel Brooks beat Scott Henry of Scotland in a playoff to win the event which was reduced to 36 holes due to fog.
- Sports & Recreation
- Alastair Forsyth