He is accused of sending the message to Obama, Vice President Joseph Biden, a Louisville newspaper and about 70 other people on Sept. 28.
Gimbel has not entered a plea and is scheduled to be arraigned Monday. His defense lawyer was not immediately available for comment.
The e-mail rambled on and included specific references to first lady Michelle Obama and the phrase, "do it to his children and family first in front of him. Failure to comply. That'll teach him," according to the indictment.
A similar e-mail was sent earlier in the month, according to a criminal complaint prepared by the Secret Service.
When officers interviewed Gimbel at his home, he admitted sending the first message but said he wanted to get attention, not hurt Obama, authorities said.
He was warned that he would be prosecuted if he sent any more.
The Secret Service listed a history of more volatile e-mails directed at President George Bush, Vice President Dick Cheney and the Crescent City police chief over the past two years.
In seeking an arrest warrant, authorities asked for permission to enter Gimbel's house without knocking because sheriff's deputies had found him with a loaded handgun during an earlier arrest and some of his e-mails included threats against law enforcement officers.
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