It was written in 1937 to the mayor of Kendal, to reassure him that she would take care of the town's last working loom, which she had just bought.
She also congratulated him on the Cumbrian town's purchase of a prayer book once owned by Henry VIII's wife Catherine Parr - included in the lot.
The letter was signed Beatrix Heelis, after the writer's  marriage in 1913.
Kendal-based 1818 Auctioneers had estimated the lot would fetch between £1,500 and £2,000.
The then 71-year-old author started the letter "you may remember my name" and goes on to reassure the mayor, Henry Airey, that she "will not take away a relic of Kendal without telling you".
The letter and prayer book were put up for sale by descendants of Mr Airey.
A spokesman for the auctioneers described the letter as "a delight to read".
The name of the purchaser has not been revealed.
Many of Potter's creations, including Peter Rabbit and Gemima Puddle-Duck, were written in the Lake District.
Last year was the 150th anniversary of her birth.
A hand-written letter by children's author Beatrix Potter has sold for £1,800 at auction.