Selina Hony said the public had been given the impression that the family had agreed to the sale but, she said, the school had presented it with a fait accompli.
The life-sized family portrait of Ms Hony's ancestors, which was donated to the school by her father, Henry, is to be auctioned by Christie's next month.
Marlborough has said an increase in the painting's value means that it can no longer afford to keep it secure and insured. The money raised by the sale will go towards a new swimming pool and arts centre at the pounds 4,930-a-term school in Wiltshire. But Ms Hony said the decision to sell was completely against the family's wishes. She claimed the school "gave a false impression about the decision to sell the great Gainsborough portrait, and the `agreement' of the donor's three daughters.
"We are deeply upset that they have seen fit to proceed to an open sale in full knowledge of our opposition to such a course of action," she said.
The portrait depicts George Byam (1734-79) of Apse Court in Surrey, with his wife and daughter, Selina. They were a merchant family with interests in the West Indies and the painting was donated by one of their descendants, Selina'sgreat-grandson Henry Hony, in 1955. His daughter said: "Marlborough College has always played a great part in my life.
"I can understand, though with deep regret, that the College no longer feels able to secure and insure the picture. However, I and my sisters, the donor's nearest surviving family, are profoundly opposed to the sale of the picture unless it is to a gallery or museum in the UK. A sale abroad or to a private buyer would not be in keeping with our father's wishes. I feel that Marlborough gave the impression that we were happy for it to go abroad and that is not the case."
A spokeswoman for Christie's said both the Tate and the National Gallery had been approached about buying the painting but it had not been possible to raise the money at such short notice. Unless another public institution can find the estimated sale price of pounds 3m it is likely to go abroad.
The 2.5-metre by 2.3-metre painting is one of Thomas Gainsborough's most important works from his time in the fashionable spa town of Bath. He moved there in 1759 and almost immediately became the most sought- after artist in the town until he moved to London in 1774. The Byam family painting is the most successful of his group portraits from that period.
Marlborough College yesterday declined to comment on the matter but a spokeswoman for Christie's said it was still trying to find a home in the UK for the painting, which she added had been donated by Mr Hony "unconditionally".
"We are pursuing a few lines of inquiries with galleries but it is likely that it will be in the sale and we don't know who will buy it," she said.
"The school felt that it was just hanging in a locked room and no one looked at it and because it needs to be kept under special conditions, they felt it should go to someone who will be able to look after it. The money will go towards the education of all the pupils."Reuse content