At one point, its share price fell more than 10% on the Milan stock market. By mid-afternoon, it was still 9% down.
The bank said the ECB had given it until 3 October to draw up a plan for reducing non-performing loans.
Italian banks are saddled with €360bn (£300bn; $400bn) of bad debt, about a third of the eurozone's total.
Monte dei Paschi accounts for €46.9bn of that total.
In a draft decision sent to the bank by the ECB, it was told to reduce gross non-performing loans from €46.9bn to €32.6bn by 2018, representing a cut of 30% over the next three years.
Investor concern over the strength of the industry has hit Italian banking shares this year.
Several other Italian banks also suffered big share price falls on Monday.
In April, Italy's financial industry approved a government-backed plan to set up a rescue fund to help weaker banks.
The Atlante fund will be made up by private money, reportedly worth €5bn, and will buy up shares and bad debt in struggling banks.
Shares in Italy's third-biggest bank, Monte dei Paschi di Siena, have slumped after the European Central Bank told it to reduce its debt burden.