He and four others were held as part of an investigation into the awarding of building contracts in the city.
It is understood the Labour Party has suspended Mr Anderson pending the outcome of the case.
The year-long police probe, Operation Aloft, has focussed on a number of property developers.
Liverpool City Council said it was co-operating with Merseyside Police.
A police statement said those arrested include two men, 33 and 62, both from Liverpool, on suspicion of conspiracy to commit bribery and witness intimidation.
A 46-year-old man from Ainsdale has also been arrested on suspicion of the same offence.
The other two arrested men are a 72-year-old man from Liverpool and a 25-year old from Ormskirk, who have been arrested on suspicion of witness intimidation.
Developer Elliot Lawless was arrested in January 2019 and denied any wrongdoing. Elliot Lawless is currently released under investigation and was not one of the five arrested earlier on Friday.
Councillor Richard Kemp, leader of the opposition Lib Dem group on Liverpool City Council, said Mr Anderson "should follow the precedence set by leaders of the council and other senior figures in such cases."
"He should step away from the council and step away from his mayoralty while this goes through due legal process," he said.
Mr Anderson joined the Merchant Navy after leaving school aged 16.
He later studied for a degree in social work at Liverpool John Moores University and went on to become a social worker for Sefton Council in 1992.
The father-of-four was Liverpool's first elected mayor in 2012 having served on the city council since 1998.
His national profile been raised by his role in driving forward mass coronavirus testing in the city.
Mr Anderson, whose brother Bill died recently of Covid-19, was praised for his response to the virus by Prime Minister Boris Johnson.
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