Anderson and four others were arrested last Friday as part of an investigation into building and development contracts in the city.
All five were released on bail pending further enquiries as the year-long investigation “Operation Aloft” continues.
Anderson said: “I have always done what I believe is best for the city, and I am taking the following action with those best intentions in mind.
“It is important that everyone in Liverpool knows that our leaders are focused on what is most important to the people; their livelihoods and, with a pandemic still in force, their lives.
“For this reason, I believe it is important that the city, and government, are reassured that our city is indeed operating in the correct way.
“I am, therefore, stepping away from decision-making within the council through a period of unpaid leave, until the police make clear their intentions with the investigation on the 31st December.
“I will make a further statement at that point. Wendy Simon will be acting as Mayor and I have all faith that she will provide the leadership our city requires at this time.”