The letter was delivered into the mailbox of its Vienna office, AOC general secretary Peter Mennel said.
He added: "We have immediately alerted the Federal Criminal Agency, which is investigating the case."
The AOC said in a statement it was "not regarding it as an acute threat at the moment".
Mr Mennel discussed the matter with Flock as they were sharing a flight from Vienna to Sochi, carrying many of the 130 Austrian Olympians on board.
He said: "She is not worried. She trusts in our security measures."
Schild is scheduled to travel to Russia next week as she will only compete in the women's slalom on February 21.
Schild, who won silver in slalom in Vancouver four years ago, is set to compete in her fourth Olympics while it is Flock's first Olympic appearance.