The 33-year-old former cruiserweight world champion was set to fight France's 2016 super heavyweight Olympic champion Tony Yoka in Paris on Saturday.
"(On Monday), the Voluntary Anti-Doping Association (VADA) informed Queensberry that Lawrence Okolie returned an adverse finding following an anti-doping test conducted ahead of the show in Paris this Saturday," the promoter said in a statement.
"A further update regarding the event will be made in due course."
Having moved up to heavyweight at the end of 2024, the Briton has fought three times in the division, winning all three bouts. He is ranked seventh in the world in the division by boxing website Boxrec.
Okolie has an overall record of 23 wins, including 17 knockouts, and just one defeat.
Tuesday's press conference, scheduled to take place in Paris to promote the bout, was cancelled at the last minute following the result of the test.
The promoters said they were, among other things, looking into the possibility of finding another opponent for Yoka, who has a professional record of 15 victories and three defeats.