Frances Burman fractured her hip in the fall from a chair.
The 80-year-old was a resident at the Shrewsbury's Maesbrook Care Home.
Because of her mobility problems, two people were needed to attend to Mrs Burman when she had a shower.
But following her death an investigation by the Health & Safety Executive revealed that while two carers were attending to Mrs Burman, only one was directly involved in helping her in the shower.
The fine was imposed on Maesbrook Care Home Ltd at Shrewsbury Crown Court after it admitted an offence under the Health & Safety at Work Act of exposing a non-employee to a risk to their health and safety. The home, in Church Road, Meole Brace, must also pay the £14,725 costs.
Judge Jim Tindal said the circumstances indicated that it was only in hindsight that it was apparent the interpretation of the risk assessment was wrong.
Judge Tindal said evidence showed Maesbrook was regarded as a good care home and the operators had taken immediate responsibility for what happened and offered genuine remorse.
Miss Michelle Heeley, prosecuting, said Mrs Burman, known as Nita, moved to Maesbrook in 2011 having suffered a stroke in 2008 which left her with limited mobility.
She had to be assisted in and out of bed, or chair with the use of a sling or hoist and required assistance in all aspects of washing and bathing.
On September 8, 2014, Mrs Burman suffered a fall and fractured her hip and her condition deteriorated and she died on September 26 – just four days after her 80th birthday.
Miss Heeley said that a subsequent post-mortem confirmed the cause of death to be cardio-respiratory failure, a fractured neck of the left femur, a fall and coronary atherosclerosis.
Mr Peter Smith, for Maesbrook, said his client was genuinely sorry for the breach and had done much to address issues raised.