Gillian Louise Dicks, 41, of the Sydney suburb of Forestville, had pleaded guilty to aggravated indecent assault and three counts of sexual intercourse with a child aged between 10 and 14.
Two of the counts related to digital penetration and the third to oral sex.
In the NSW District Court today, Judge Robert Toner sentenced her to a minimum of 2½ years in jail and a maximum of 4½ years.
He referred to a "moving and disturbing" victim's impact statement made by the girl.
"I can only hope the residual effects of the offence on you [the victim] will modify with time," he said.
The girl had believed she was in a "relationship" with Dicks, who told her she would probably go to jail for a long time if their sexual relationship was revealed.
The judge accepted that Dicks was remorseful and had excellent prospects of rehabilitation.
He noted that at the time of the offences Dicks had problems with alcoholism, chronic major depression and post-traumatic stress disorder.
"As a police officer she had been exposed to traumatic incidents, which to a large extent were left unaddressed," he said.
But the offences had been a "gross breach of trust", Judge Toner said, noting Dicks originally came into contact with the girl's family as a result of her duties as a police officer.