The six-day test, involving Red Bull's troubled engine supplier Renault, reportedly occurred between the last pre-season track test in Bahrain and the start of the season in Australia.
Rumours of the illegal test reportedly began to circulate after someone circulated correspondence to the FIA as well as the Mercedes, Ferrari and Sauber teams.
Germany's Auto Bild reports that the test actually involved Red Bull's junior team, Toro Rosso, who have been deeply involved in the efforts to pull Renault out of its pre-season technical crisis.
But Red Bull test driver Antonio Felix da Costa had 'tweeted' in early March that he was headed to Austria for a '5 day trip'.
"Spending the weekend in Graz, Austria," he added two days later. "Not by choice though!"