The governor's request came after politicians in Graz began a petition drive to rename the stadium, reacting to Schwarzenegger's decision last week to deny clemency to condemned inmate Stanley Tookie Williams. Opposition to the death penalty is strong in Austria.
In a letter that began "Dear Mister Mayor," Schwarzenegger said he decided to spare the Graz city council "further concern" should he be forced to make other clemency decisions while he's governor. Another inmate is scheduled to be executed in California Jan. 17.
"In all likelihood, during my term as governor, I will have to make similar and equally difficult decisions," Schwarzenegger said in the letter. "To spare the responsible politicians of the city of Graz further concern, I withdraw from them as of this day the right to use my name in association with the Liebenauer Stadium."
The stadium was renamed for the former Hollywood star in 1997. He asked that the lettering be removed by year's end.
Schwarzenegger spokeswoman Margita Thompson said the letter was faxed Monday to the Graz city hall. The city council was expected to take up the matter next month.
In the letter, Schwarzenegger also said he would no longer permit the use of his name "to advertise or promote the city of Graz in any way" and would return the city's "ring of honor."
The ring was given to him in a ceremony in Graz in 1999. At the time, Schwarzenegger said he considered it "a token of sincere friendship between my hometown and me."
"Since, however, the official Graz appears to no longer accept me as one of their own, this ring has lost its meaning and value to me. It is already in the mail," the governor wrote.
Williams, co-founder of the Crips gang, was convicted of four 1979 murders. He was executed shortly after midnight Dec. 13.