Hien Minh Nguyen, who served in the northern Californian city of San Jose until taking leave in December 2013, has been charged with 14 counts of bank fraud and 4 counts of tax evasion.
Mr Nguyen's alleged to have failed to declare more $1m (£672,000) of his income between 2008 and 2011.
He's also alleged to have put $19,000 (more than £12,700) worth of cheques given to him by fellow Christians for the Vietnamese Catholic Centre in the area, which he led, into his own bank account.
Bishop Patrick McGrath, from the Diocese of San Jose, said in a statement: "The diocese has been cooperating with an ongoing criminal investigation by the Internal Revenue Service into the conduct of Monsignor Hien Minh Nguyen since October of 2012.
"Any facts in the matter are the part of the investigation, and only the IRS has the authority to make disclosures at a time of its choosing.
"We do not know when that might be. At the request of the IRS, we have had minimal direct communication with Monsignor Hien. He is on a personal leave of absence, which he requested."
Hien Minh Nguyen is yet to enter a plea, and is scheduled to reappear in court in on Tuesday where proceedings continue.