The Central Weather Bureau urged the public to take precaution against downpours even though the storm was not likely to make landfall.
The warning prompted authorities to cancel ferries between Taitung and two offshore scenic spots, Green Island and Orchid Island, Taitung county government officials said.
As of 11.30 in the morning, the storm was 430 kilometres southeast of the island's southern tip, the bureau said.
Packing gusts of 101 kilometres per hour, Kong-Rey was moving north-northwest at 13 kilometres per hour, it said.
