"There are too many Republicans in this race and the people of our state simply cannot risk a continuation of the Gray Davis legacy. For these reasons, I think it is wise to step aside," Simon said in a videotaped statement.
He did not endorse Arnold Schwarzenegger or any other candidates in his one-minute statement.
Simon lost to Davis in last fall's general elections and was one of 135 candidates seeking to replace him. Simon lost that race to Davis by just 300,000 votes in a state with 1 million more Democratic voters than Republicans.
Voters will decide October 7 whether to recall Davis and, if so, who should replace him in the governor's office. The recall was triggered by voter anger over the state's economic and energy woes.
Notable deaths of 2014 [PHOTOS]