Fresenius pulled the plug on plans to take over Rhoen-Klinikum, discouraged by healthcare industry investors who had sought to prevent the emergence of a dominant private-sector hospitals operator in Germany.
Rhoen shares tumbled 19.5 percent at the open, while Fresenius shares traded 1.9 percent higher.
Freseniussaid in a statement on Monday it would not launch a renewed takeover offer "for the time being".
"We regret that our public offer was blocked without providing a constructive alternative," Chief Executive Ulf Schneider said.
"All our investments must add value, with manageable risks. After thorough analysis, we have therefore reached the conclusion that a new offer cannot be justified."
Rhoen said it regretted the decision as it remained convinced of the benefits of merging two large private clinic operators in Germany, adding it would seek to play an active role in the consolidation of the market.
German healthcare conglomerate Fresenius in April unveiled plans to buy Rhoen in a deal worth 3.1 billion euros ($3.9 billion) and fold it into its own hospitals unit Helios, combining two of the three largest private-sector hospital chains in Germany.
But in June, German hospital group Asklepios effectively blocked the bid by buying a more than 5 percent stake in Rhoen. As a result, Fresenius fell short of the 90 percent approval it needed among Rhoen shareholders.
B. Braun, which competes with Fresenius in medical equipment such as infusion and tube feeding supplies, followed up by buying a 5 percent stake in Rhoen.
The group is said to be against the tie-up because it risks losing an important client if Rhoen becomes part of Fresenius' hospitals division.
Although caving in for now, Fresenius said it would raise slightly its stake in Rhoen of currently 5 percent minus one share, it said.