According to Interpol's website, Mohammad Yaqub Haidari, 52, is wanted for "large-scale tax evasion, fraudulent conversion" in a case dating back to 2003.
"We have started our investigation based on Afghan law. If this accusation is proved, he will be removed from the list of cabinet nominees," presidential spokesman Nazifullah Salarzai told AFP.
Afghanistan's new cabinet was unveiled on Monday after three months of wrangling following the election of Ghani and the formation of a "national unity government" in the wake of last year's fraud-mired polls.
The names of the 25 new ministers have already been sent to parliament where lawmakers will vote for them on Tuesday.