The state government said the two deaths were a 63-year-old diabetic woman in the hilly interior of Rio de Janeiro state and a 69-year-old man, also diabetic, in the city of Niteroi.
President Jair Bolsonaro, who has faced criticism for his lax handling of an outbreak he initially called a "fantasy," issued a decree restricting entry of foreign visitors at land borders with Argentina, Paraguay, Bolivia, Peru, Colombia, Suriname and French Guiana. On Wednesday, Brazil began turning away Venezuelans at the border.
Brazil had reported 428 confirmed cases of the virus as of Wednesday evening, more than doubling in three days.
Responding to the latest deaths, Rio Governor Wilson Witzel urged people to stay indoors and to avoid gyms and beaches.
Brazil's major cities have moved to restrict social gatherings in an attempt to slow the outbreak, with shopping malls and nightclubs asked to close. But the measures remain inconsistent between cities and states.
Brazil's benchmark Bovespa index slipped as much as 7% to a nearly three-year low before paring losses as U.S. markets recovered on pledges of economic stimulus from Washington.
The rapid spread of the virus represents a major threat for the far-right populist Bolsonaro, who was already struggling to resuscitate the country's weak economy.
On Wednesday night, Brazil erupted to the sound of banging pots and pans and shouts of "Bolsonaro out!" with housebound protesters expressing their anger toward the president for the second night in a row.
By Pedro Fonseca