Annus, who has denied any wrongdoing, gave a negative test after winning the hammer competition at the Games on Sunday. He then returned home, in apparent contravention of regulations, and announced his retirement.
The IOC said on Friday they had asked Hungarian officials to find Annus so they could test him again for drugs for an out-of-competition sample.
The Hungarian Olympic team in Athens said Annus had been asked to report for a test before noon, and then on the Austrian side of the border between Hungary and Austria by 4 p.m. local time (1400 GMT).
"The information we have now is not in compliance with the regulations," official Gyorgy Bakanek, a doping expert, told Hungarian news agency MTI.
"Although tests are possible during the whole period of the Olympics ... this usually concerns athletes who are still staying there and have not competed yet.
"There has been no example until now for additional testing of someone previously tested negatively under formal circumstances"
Annus, 31, shared a coach with Hungary's discus gold medallist Robert Fazekas, who was expelled from the Games after refusing to provide a complete urine sample after Monday's final. Fazekas had to return his medal.
The IOC dispatched two medical supervisors to Annus's home in western Hungary on Thursday to collect a sample for testing.
"The (two) supervisors asked police to protect them as on Thursday evening they felt themselves being threatened by a company who appeared with cars and motorcycles at the house of
Adrian Annus in Jak (western Hungary)," Vas county police spokesman Ferenc Szalai told Reuters. "They received a police escort and went to the house again today, but they did not find (Annus) at home and left."