The direction in this regard was issued by the court on a petition filed by A K Shaji alleging that Joseph had amassed wealth worth about Rs 18 lakhs as a minister in the previous Oommen Chandy government.
The detailed report has to be filed by November 29.
Joseph, his wife and son are respondents in the case.
Reacting to the court order, Joseph said he would "fully cooperate" with the investigation.