Venezuelans desperately rushed to banks Tuesday to dump cash after the government announced it is eliminating the largest circulating bank note to combat contraband in a country whipsawed by the world’s deepest recession and highest inflation.

In the financial district of downtown Caracas, National Guard troops carrying assault rifles stood outside banks as crowds of people lined up to deposit stacks of 100-bolivar bills, which President Nicolás Maduro said Monday would become void on Wednesday night. In the provinces, where...