RIO DE JANEIRO—Brazil’s worst recession in recent history continued into 2016, data showed Wednesday, as rising unemployment and deepening political turmoil dragged the once-dynamic economy into its fifth consecutive quarter of decline.

Gross domestic product shrank 0.3% in the first quarter of 2016 from the previous three months in seasonally adjusted terms, the Brazilian Institute of Geography and Statistics, or IBGE, said. That was better than expected, as the median estimate in a Wall Street Journal survey of eight economists...