The Dow Jones closed 260.51 points, or 1.5%, lower to 17,140.24.
The S&P 500 was down 36.87 points or, 1.8%, to 2,000.54, while the tech-heavy Nasdaq fell 113.54, 2.4% to 4,594.44.
Bank stocks were particularly hit as questions emerged about London's future as a global finance capital.
"The UK's status as a major international banking hub could be damaged as some business lines shift to the EU,"  warned ratings agency Fitch, which downgraded the UK's credit rating to 'AA' on Monday.
Shares in Bank of America and JP Morgan fell 6.3%, while Citigroup fell 4.5%.
"The market is reflexively going to sell down the banks early," George Maris of Janus Capital told the BBC.
"The banks will suffer, but they are much more solvent than they were in the financial crisis so it does feel like the bank sell off will end."
The US dollar rose to a 30-year high against the pound, with Â£1 buying $1.32.
Shares in credit card company American Express fell 4%.
Aircraft maker Boeing also saw a drop in its share price following a fall on Friday. Boeing shares were down 3%.
Not all stocks were falling. Tech firm Twilio was up 3.6%.
Twilio shares began publically trading on the stock markets last week and rose over 90% on their first day.
Shares of gold producers were also higher as investors flocked to gold as a safe haven.
Alamos Gold rose 4.3% and Anglogold Ashanti climbed 4%.
(Closed): Shares on Wall Street closed sharply lower, following a global sell-off, as the impact of the UK's decision to leave the European Union continued to unsettle investors.