Huizar's campaign spokesman, Michael Trujillo, sent the e-mail Friday.
"We are about to put a political bullet in between Rudy Martinez's forehead and make him pee in his pants too," the e-mail said.
Eagle Rock businessman Rudy Martinez is running the March 8 election for the city council seat on Los Angeles' east side held by incumbent Huizar.
The e-mail comes just weeks after Congresswoman Gabrielle Giffords was shot in the head in Tucson, Ariz. Martinez said he feels threatened.
"The fact that the councilman fired his campaign manager over this is quite not enough for me," Martinez said. "I didn't receive an apology and I'm scared for my own life, I'm scared for my family. It's sad that politics had to come to this."
A Huizar campaign official issued a statement Sunday.
"I became aware of Mr. Trujillo's e-mail this morning and immediately terminated his relationship with our campaign," the statement said. "The remarks were inappropriate, disrespectful and offensive. On behalf the campaign, I apologize to Mr. Martinez for this breech."
Trujillo apologized for his remarks.
"I made a mistake and am taking responsibility for my actions," Trujillo said in a statement. "I am sorry if my actions reflect badly on Councilmember Jose Huizar, a truly effective leader and a man of great integrity."