"Yes, it is true, Ajunwa failed a drugs test at a recent meeting in Greece," said Nigerian athletics boss Dan Ngerem.
The official refused to disclose which banned substance Ajunwa used, saying that the athletics federation was awaiting the result of the B sample of the test.
Under international athletics rules, any athlete who tests positive for drugs twice would automatically be banned for life.
Ajunwa (31) won gold in the long jump at the Atlanta Olympics in 1996 with a leap of 7.12 metres.
She first served a four-year drugs ban in 1992 after testing positive for anabolic steriods.
Ajunwa, who is a police officer, has threatened to sue a company which sponsored her training and which allegedly gave her substances she thought were innocent but which contained banned substances.
"As a disciplined officer and athlete, I would never involve myself in anything that would tarnish my image and that of the Nigerian Police Force", Ajunwa said in a letter to Nigeria's police chief.
She added: "I am now considering taking legal action against the company (which has been sponsoring her training) while appealing to the IAAF over my last dope test."
Police spokesman Haz Iwendi told reporters that the police will stand by Ajunwa.
"We believe her, though we are yet to get the full report. She has always done Nigeria proud," he said. - Sapa-AFP