John Cryan told them the bank had become the object of "hefty speculation" and that "new rumours" were causing the share price to fall.
He said the bank's reserves and profits underlined its strength.
The shares had fallen again on Friday, but closed 6.4% up on rumours that a huge US fine could be reduced.
In his letter, Mr Cryan pointed out that Deutsche had €215bn in reserves and made €1bn in profits for the last six month. At no point in the last 20 years had Deutsche been as strong as it is now, Mr Cryan insisted.
"The release of the memo... seems to have taken the edge off of the German company's dramatic" share price decline, said SpreadEx analyst Connor Campbell.
At the start of trading on Friday, Deutsche's share fell 9%. That followed a big fall overnight in the bank's Wall Street-listed shares, a drop sparked by reports that some hedge funds had withdrawn money from the bank.
Deutsche Bank is under the most pressure of any bank since the financial crisis.
Investors are increasingly worried about the financial health of the bank, which faces a $14bn fine in the US for mis-selling mortgage-backed bonds before the financial crisis of 2008.
The bank's shares have been falling steadily from a recent high of €27.80 last November. But at their peak in May 2007, before the start of the banking crisis, the shares were valued at almost €100.
Earlier on Friday, the chairman of the Eurogroup of eurozone finance ministers, Jeroen Dijsselbloem, said the penalty was excessive.
"The $14bn are going to the American authorities. I don't begrudge the American authorities that money, but it is money that has to be paid by European account holders and investors. The fine is too high," he said.
However, Deutsche's shares closed up 6.4% on Friday, following unconfirmed reports that the bank was close to agreeing a reduction in the fine with the US Department of Justice.
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Deutsche's woes hit bank shares across Europe. German rival Commerzbank was down about 6%, while the shares in UK, Swiss, French and Italian banks also suffered.
In Italy, Economy Minister Pier Carlo Padoan told La Stampa newspaper that it was in everyone's interest "to look for solutions that must then be carefully handled".
But the German government's position is not clear.
Although a newspaper report earlier this week suggested the German government had made some provisional plans to rescue Deutsche, this would be politically unpopular.
Eckhardt Rehberg, parliamentary budget spokesman for Chancellor Angela Merkel's conservative CDU party, told Reuters: "At the present time, I would rule out any capital help. That would not be the right way to go."
Mr Dijsselbloem ruled out a government bailout should the bank face bankruptcy. "We have set ourselves the rule that a bank needs to solve its own problem and if necessary the buck stops with the investors, the share holders, the bond holders and not with the authorities," he said.
"This is a very important principle of the (European) banking union and it has to remain that way. Fortunately, the German government feels the same way," he added.
Deutsche Bank made a net loss of €6.8bn last year and has embarked on a round of hefty cost-cutting that includes shedding 15% of its 100,000-strong global workforce.
Like most of the world's leading banks, Deutsche Bank has been embroiled in the major banking scandals of recent years, including rigging interest rates.
The chief executive of troubled Deutsche Bank has emailed the 100,000 staff to reassure them that the German giant's finances are strong.