Ackermann said the family of chief financial officer Pierre Wauthier, who had worked at Europe's No. 3 insurance group for 17 years, believed he shared some of the blame for his death.
Wauthier's death came just weeks after the head of telecoms firm Swisscom, Carsten Schloter, died in another apparent suicide. The deaths have shocked corporate Switzerland and prompted calls for greater support for boardroom high-fliers.
"I have reasons to believe that the family is of the opinion that I should take my share of responsibility, as unfounded as any allegations might be," Ackermann said in a statement, adding that he wanted to avoid any damage to Zurich's reputation.
Swiss police said that Wauthier - who was found dead at his suburban home near Zug on Monday - appeared to have committed suicide.
A spokeswoman for Zurich Insurance did not elaborate on what allegations Ackermann was referring to surrounding Wauthier, who was 53 and left a wife and two children.
Wauthier's widow declined comment on Thursday. And at the family's lakefront home, once a traditional Swiss inn, a security guard said relatives did not wish to talk.
Zurich's chief executive Martin Senn said he was not aware of any dispute that could have driven Wauthier to his death.
"We didn't spot any conflicts that could or should have led to such a death," Senn told Swiss television.
However, a former colleague of Wauthier's said there was pressure within the company to increase its share price.
Two insurance executives outside the firm's headquarters in Zurich described their colleagues as "somewhat shellshocked" and said Ackermann's departure was a surprise for the industry.
Zurich said Vice-Chairman Tom de Swaan would take over as acting chairman.
One of Europe's leading economic power brokers, Ackermann, 65, transformed Germany's Deutsche Bank and played a role in the euro zone's financial crisis as chairman of the Institute of International Finance (IIF).
He was touted as a candidate for top financial jobs in his native Switzerland before he took the relatively low-key role at Zurich last year. He also sits on the boards of Royal Dutch Shell, Siemens and Investor AB.
Ackermann has survived controversy before. In 2006, he paid 3.2 million euros, without admitting wrongdoing, to avoid trial in a dispute over payments to executives at telecoms firm Mannesmann, where he sat on the board of directors.
One of few senior industry figures to keep his job through the current financial crisis, he became a forceful public advocate for the Swiss financial sector after leaving Deutsche.
"Ackermann's mission when he came was to shake up Zurich, to infuse a more dynamic mentality into it," said a person close to the former Zurich chairman.
"Yes, insurance isn't banking. But there was still more oomph to be wrung out of Zurich, he thought."
When Ackermann took over as Deutsche Bank chief executive in May 2002, radical surgery was needed. Burdened with high costs, it was slipping as one of the largest lenders in Europe.
The first non-German to lead the bank, Ackermann was asked to transform it into a "global champion", but fell out with a German establishment that saw Deutsche's traditional role as supporting national industries.
When Ackermann joined the Frankfurt-based institution, the bank derived more than 70 percent of revenues from Germany. Ackermann sold off industrial holdings and slashed jobs, and Deutsche now makes less than 30 percent of its revenue there.
However, his arrival at Zurich failed to impress investors and there was considerable change in the top ranks.
Former general insurance head Mario Greco left a year ago to become head of Italian insurer Generali. Two weeks ago the head of its life insurance arm, Kevin Hogan, left to become AIG's head of consumer insurance.
On August 15, Zurich said it would be hard pressed to meet certain performance targets after posting a 27 percent fall in second-quarter net profit due to natural disaster payouts, which topped those of European rivals because of its high exposure to the United States.
The shares closed down 2.47 percent at 228.80 francs, but remained above the low of 225.6 francs that they reached on Tuesday after news of Wauthier's death. The volume of shares traded on the day, however, was the highest in over three years.
(Additional reporting by Martin de Sa'Pinto and Alice Baghdjian in Zurich and Edward Taylor in Frankfurt; Writing by Tom Miles; Editing by Peter Graff, Alexander Smith and Alastair Macdonald)
By Katharina Bart