Shetland's ballot boxes had to be unloaded from the aircraft when it was called upon to take a pregnant woman to hospital in Aberdeen.
Returning officer Alistair Buchan said contingency arrangements had been investigated, but no alternative to the Loganair Islander craft had been available.
After consulting the five candidates, he announced that the count in Kirkwall would be suspended until 0900 BST on Friday.
Voting slips from polling stations on Orkney's mainland and South Isles had already been counted when the suspension was announced.
The plane was due to return to Shetland after flying the woman to Aberdeen.
It will pick up the boxes, and will arrive in Orkney at around 0530 BST.
"I apologise for the inconvenience, but there was nothing we could do about it in the circumstances," said Mr Buchan.
Liberal Democrat candidate Alistair Carmichael is hoping to succeed Scottish Lib Dem leader Jim Wallace as MP in the Orkney and Shetland constituency.
He said: "It's unfortunate, but these things happen in island communities."
Earlier, the result of the Cunninghame North seat in Ayrshire was delayed by almost two hours after a helicopter due to pick up ballot boxes from the Isle of Arran was sent on a rescue mission.
The helicopter from HMS Gannet at Prestwick was called out to the rescue in the north of Scotland.
The returning officer had to rely on a back-up plan to collect the votes by chartered boat.
Labour's Hadley Dearne held the seat with a majority of more than 10,000 over the Scottish National Party's Louise Page.