The letter was delivered Monday into the mailbox of its Vienna office, AOC general secretary Peter Mennel said Tuesday.
"We have immediately alerted the Federal Criminal Agency, which is investigating the case," Mennel said.
The AOC said in a statement that it was "not regarding it as an acute threat at the moment."
Mennel discussed the matter with Flock as they were sharing a flight from Vienna to Sochi on Tuesday, carrying many of the 130 Austrian Olympians on board.
"She is not worried, she trusts in our security measures," said Mennel, adding that Austrian athletes will be accompanied by task force Cobra when they leave the Olympic Village.
Schild is scheduled to travel to Russia next week as she will only compete in the women's slalom on Feb. 21.
Schild, who won silver in slalom in Vancouver four years ago, is set to compete in her fourth Olympics. She also won silver in the combined event and bronze in slalom at the 2006 Turin Games.
In December, Schild captured the all-time record for most World Cup slalom wins by a female skier as she won her 35th event in Lienz, Austria.
Flock, who is set to make her first Olympic appearance, won the European skeleton title last month by coming first in a World Cup event in Koenigssee, Germany, which also counted as the annual European Championships.
The threat against Schild and Flock comes less than two weeks after a string of European Olympic committees, including Austria's, received emails containing terrorist threats against its athletes in Sochi. However, the menacing messages were deemed a hoax by security experts, who said such threats were common ahead of big events, and local organizers described them as "not real."