The investors were reacting to a $14-billion fine demand from the US Department of Justice (DoJ) and conflicting reports in German media over whether Berlin would come to the troubled bank's aid if necessary, which have sapped the bank's market valuation since Monday.
Just after 0800 GMT, shares in the bank had shed 6.35 percent to €10.90, while traditional Frankfurt rival Commerzbank - which itself announced a far-reaching restructuring this week - was also pulled down, losing 6.37 percent to trade at €5.45.
The DAX 30 index of leading German shares fell 1.5 percent.
Across Europe, banking stocks including Societe Generale in Paris, Barclays in London, Unicredit in Milan and Santander in Madrid lost between four and five percent in the first hour of trading.
"The risk perception by investors is worsening," IG France analyst Alexandre Baradez told AFP in Paris. The reports of fund withdrawals "ignited the powder", he said.
Deutsche shares had lost seven percent in New York on Thursday before trading on Wall Street ended, while markets in Hong Kong and Tokyo lost ground at open on Friday morning over worries for Deutsche's future.
Assurances from chief executive John Cryan in a Tuesday interview that a state bailout was "not on the table" and denials from Chancellor Angela Merkel's office that a rescue plan was in the works have failed to allay investors' fears.
"Mantra-like attempts to calm things down from the government, regulators and Deutsche Bank itself are being seen by investors almost as a contrary indicator," analyst Clemens Bundschuh at LBBW bank said.
Bloomberg News reported on Thursday that about 10 hedge funds that clear trades with Deutsche Bank withdrew some excess cash and derivatives holdings and moved the assets to other firms this week, citing an internal bank document.
AFP sources knowledgeable of the situation confirmed that 10 hedge funds had pulled funds out, including Millennium Partners, Capula Investment, and British fund Rokos Capital Management.
Bloomberg said that the "vast majority" of the bank's clients have made no changes to their exposure at the bank, a position echoed by Deutsche itself when it insisted that some 800 remaining customers trusted in its "stable financial position".
Deutsche has said that it will not have to pay the full amount demanded by the DoJ over its role in the devastating subprime mortgage crisis, pointing to US banks that negotiated much lower settlements.
But investors fear that the fine could still be large enough to wipe out the $5.5 billion in provisions the bank has set aside for legal entanglements.
The subprimes case is just one of 8,000 burdening Deutsche Bank, with an investigation by New York regulators over allegations of money laundering at its Moscow office looming on the horizon.
Both Deutsche and Commerzbank were among the worst performers in a European Banking Authority stress test of large banks whose results were released in July, although both insisted the exercise had demonstrated their resilience to future crises.