The moves by the Greek authorities came after the European Central Bank decided not to extend emergency funding.
London's FTSE 100 index fell 2% in early trade. Earlier in Asia, Japan's Nikkei index fell nearly 3%.
On the currency markets, the euro had fallen to $1.0953 at one point in Asian trading from $1.1165 on Friday, but it then recovered some ground.
Elsewhere in Europe, Germany's Dax share index and France's Cac 40 were both down more than 3%. The Athens Stock Exchange and Greek banks are closed all week.
Greece is due to make a €1.6bn payment to the IMF on Tuesday - the same day that its current bailout expires.
Last week, talks between Greece and the eurozone countries over bailout terms ended without an agreement, and Prime Minister Alexis Tsipras then called for a referendum on the issue to be held on 5 July.
At the weekend, the Greek government confirmed that banks would be closed all week, and imposed capital controls, limiting bank withdrawals to €60 euros (£42) per day.
