The district council spent all of its discretionary housing payments budget in the year to March, new figures show.
Discretionary housing payments are paid by local authorities to cover shortfalls in residents' housing benefit or Universal Credit.
The Government gives a pot of money to each council to make these payments, but councils can top it up with their own funds.
Despite this, many councils have struggled to stick to their budget across England and Wales, with some more than doubling their allocation.
The Government has frozen housing benefit for the last three years, and Shelter said benefits must be uprated to track the dramatic increase in rent over the last few years.
READ MORE: Malvern Hills house prices: How they compare to West Midlands
The housing charity said discretionary payments are only a temporary solution, and urged the Government to provide longer-term solutions, including building more affordable housing.
Department for Work and Pensions figures show Malvern Hills District Council spent £75,651 on discretionary housing payments in 2022-23.
It was allocated a budget of £75,651, meaning it spent all of its allocation.
In 2021-22, the council also spent all of its budget.
Across England and Wales, local authorities spent an added 15% of their combined allocation, with 42% of councils overspending their budget by more than 5%.
Just 11% of authorities spent less than 95% of their budget.
Polly Neate, chief executive of Shelter, said the freezing of housing benefit means "desperate families are struggling to balance the books in the overpriced and insecure private rented sector".
Ms Neate said discretionary housing payments are needed to bridge the gap between housing benefit and rent, but added they are "only a sticking-plaster solution".
"If the Government really wants to tackle the housing emergency, the Chancellor must urgently unfreeze housing benefit to help families pay their rent," she added.
"But the only long-term solution to the housing emergency is for the Government to invest in a new generation of genuinely affordable social homes, with rents tied to local incomes."
A government spokesperson said nearly £1.6 billion in funding has been given to local authorities since 2011, "providing a safety net for people struggling with rent or housing costs".
They added: "We are set to spend over £30 billion on housing support this year, on top of the significant cost of living help worth around £3,300 per household.”
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