Co-driver James Fulton was unhurt in the accident in pre-event testing last Thursday.
Breen's funeral took place in his home town of Waterford on Tuesday.
"Road conditions were slippery and the car slid off the road at a relatively low speed and made contact with a wooden fence," said team boss Cyril Abiteboul in a statement, providing details for the first time.
"A post from this fence intruded into the cabin through the driver’s side window.
"The stage was closed immediately and the on-stage medical team was rapidly on the scene.
"Craig was taken to hospital from the stage. As far as can be determined, Craig’s passing was instantaneous."
Abiteboul said Hyundai Motorsport and the governing FIA were working jointly to review the incident.
"As far as can be ascertained, there was no issue with any element of the car, the tyres or the safety equipment. The local police completed a report at the scene," he added.
Hyundai are competing in Croatia this weekend with a reduced two-car entry and a special livery as a tribute to Breen.
Breen would have been competing in his second rally of the season after finishing runner-up in Sweden in February.
The world rally championship has retired Breen's competition number 42 for the remainder of the season.
