Prosecutors are seeking forfeiture of the $1,224,888 allegedly generated by the fraud.
Zeleke hung up when called by The Oklahoman. His attorney could not be reached for comment.
Joint state, federal inquiry led to arrests
Also charged in a federal indictment was Zahid, 28, of Edmond, who was identified as the owner of Ghani Mart at 2719 NE 23 in Oklahoma City.
Zahid, who was born in Pakistan, is accused of using an almost identical scheme to defraud the food stamp program out of more than $650,000.
The money allegedly was taken from December 2007 through September 2010.
He is accused of one count of conspiracy and five counts of food stamp violations.
He also faces a maximum of five years in prison, three years' probation and $250,000 fine on each count.
Prosecutors are seeking forfeiture of the $652,614 he allegedly obtained through fraud.
Perry Hudson, Zahid's attorney, said he does not know enough about the case to comment.
Powell said the identities of the other individuals arrested Wednesday and Thursday and the amounts they were accused of taking through food stamp fraud were not immediately available Thursday afternoon.
The investigation is continuing, she said.
The arrests were the result of a joint investigation by inspector general's offices for the state Department of Human Services and the U.S. Department of Agriculture, Powell said.
Federal officials estimate between 3 and 6 percent of food stamp benefits are lost to fraud each year, Powell said.
"Oklahoma has one of the most aggressive food stamp fraud trafficking investigative units in the country," she said.