The plea came Tuesday in Superior Court, weeks after Filner was forced to resign over claims of sexual harassment by numerous women.
The victims in the case were only identified as Jane Does.
The judge says the maximum sentence is three years in prison for the felony and one year for each misdemeanor, and may be served concurrently.
Sentencing is set for Dec. 9.
THIS IS A BREAKING NEWS UPDATE. Check back soon for further information. AP's earlier story is below.
Former San Diego Mayor Bob Filner, driven from office by sexual harassment allegations, was charged Tuesday with felony false imprisonment and two counts of misdemeanor battery involving three women.
The felony count alleges false imprisonment "by violence, fraud, menace and deceit" but does not elaborate on the circumstances.
The victims were identified only as Jane Does.
Filner, 71, resigned in late August, succumbing to intense pressure after at least 17 women brought lurid sexual harassment allegations against the former 10-term congressman. He had been on the job less than nine months into a four-year term and was San Diego's first Democratic mayor in 20 years.
San Diego County sheriff's investigators had been interviewing Filner's accusers and said they would deliver their findings to the attorney general's office for possible prosecution. The state attorney general's office confirmed in August that it launched a criminal investigation.
Filner attorney Jerry Coughlan did not respond to a request for comment after the San Diego Superior Court issued a two-sentence statement describing the charges. A hearing was scheduled for 10 a.m. PDT at the downtown courthouse, only three blocks from the City Hall office that Filner occupied until stepping down Aug. 30.
Filner's former communications director, Irene McCormack Jackson, was the first woman to go public with allegations against Filner and filed a lawsuit against the mayor and the city, claiming her ex-boss asked her to work without panties, demanded kisses, told her he wanted to see her naked and dragged her in a headlock while whispering in her ear.
All nine City Council members as well as fellow Democrats called upon Filner to resign. A recall effort also was launched as more allegations surfaced.
But in a defiant farewell speech, Filner said he was the victim of a lynch mob and believed he would be vindicated if due process was allowed to run its course.
In exchange for his resignation, the city agreed to pay Filner's legal fees in a joint defense of the lawsuit, and cover any settlement costs assessed against the mayor except for punitive damages. The city - as required by state law - will also defend Filner against legal actions stemming from other alleged sexual harassment said to have occurred during his nine months in office as mayor.
City Attorney Jan Goldsmith said, however, the city will not represent Filner in any criminal case.