They instead called on the Japanese conglomerate to seek offers from potential buyers.
Hedge fund 3D Investment partners, which owns more than 7 percent of Toshiba, presented its objections in a three-page letter to the company's board.
It's the first major shareholder to oppose the break-up plan announced earlier his month.
Toshiba embarked on a strategic review after a damaging governance scandal.
A probe found it had colluded with Japan's trade ministry to pressure foreign shareholders.
It announced plans to house its energy and infrastructure divisions in one company and its hard disk drive and semiconductor business in another.
A third will manage the company's flash-memory chip company and other assets.
3D's letter, seen by Reuters, highlighted unease in Toshiba's recent weak stock performance and said it may be difficult to win full approval in a shareholder meeting early next year.
It added the break-up is unlikely to resolve any of the company's current problems and is "instead very likely to create three underperforming companies in the image of today's Toshiba."
Other shareholders told Reuters they were disappointed Toshiba had turned down the idea of going private.
A Toshiba spokesperson said it does not comment on individual exchanges with shareholders,and 3D declined to comment.
The company has said it plans to complete its overhaul by March 2024.
