The remarks add to scepticism expressed by other shareholders about the German group's plan - announced in September - to spin off its capital goods businesses.
Shares in the group have fallen by 32 percent since.
"We have our doubts whether the proposal has the desired positive effects," Elliott said in the Dec. 10-dated letter, the person said, marking the first comments by the activist investor since the transaction was made public.
Shares in Thyssenkrupp extended losses after the remarks were published by Reuters to trade 1.7 percent lower.
Elliott was not immediately available for comment. A spokesman for Thyssenkrupp declined to comment.
The letter, whose existence was first reported by Germany's Manager Magazin, was written in response to remarks by Thyssenkrupp's boss Guido Kerkhoff, who in November said he had not heard from Elliott since July, the source said.
Elliott in May said it had taken a stake of less than 3 percent in Thyssenkrupp, a move that was followed by the resignation of both the company's chief executive and chairman, two profit warnings as well as the break-up plan.
Kerkhoff is counting on full support of the plan by the group's supervisory board, including members from its two largest shareholders, but smaller investors have started to question the move to split up.
Critics fear a global economic downturn would hit the businesses Thyssenkrupp plans to hive off, and are also concerned the European Union will seek big concessions to approve a planned steel joint venture with Tata Steel.
"We maintain our conglomerate discount at 10 percent due to ongoing investigations regarding the ... JV and increased risks due to lower profitability," HSBC wrote on Thursday, keeping a "hold" rating on the stock.
The steel tie-up faces increased scrutiny by the European Commission, which has expressed concerns about the combined entity's position in packaging and automotive steel and pushed back a deadline to rule on the deal to late April.
Should the break-up plans collapse, investors are expected to focus on restructuring Thyssenkrupp's elevator unit - its most profitable business - again, be it via a sale, partial listing or a joint venture with a rival, most likely Finland's Kone.
(Reporting by Christoph Steitz; Editing by Maria Sheahan and Mark Potter)