Audrey Allen, 80, died in hospital a month after repeatedly falling at The Grange Care Home in Eckington in March 2016.
At Chesterfield Magistrates' Court, Derbyshire County Council admitted failing to provide safe care and treatment.
Ms Allen, a former nurse, fell while in a communal area at the home and the staff moved her to her bed. Though she reported pain in her left side, no medical advice was sought. She had suffered rib fractures, which lacerated one of her lungs, leading to a haemorrhage.
No assessment of the pensioner's needs had been carried out by staff and no measures had been put in place to protect her, despite her being a high-risk resident. There was also a shortage of senior staff due to restructuring by the council.
Judge Jonathan Taaffe said the fine would have been more had the authority not entered an early guilty plea, and questioned how it could have been allowed to happen at a care home rated as "good".
The prosecution is the first the Care Quality Commission (CQC) has brought against a local authority since it was given powers to prosecute health and social care providers for failing to provide safe care and treatment back in 2015.
A spokesperson for the council said it had reviewed and revised its falls policy.
Rob Assall-Marsden, interim deputy chief inspector for adult social care for the CQC, said: "This is a distressing case and our thoughts and sympathies are with Miss Allen's family. We hope this result sends a message to other care home providers that they must ensure people's safety at all times and manage any risks to their wellbeing."