Most of the injuries and arrests came in Quito, the epicenter of Thursday's protests, deputy minister for domestic security Diego Fuentes told a TV station.
In the capital city, demonstrators with sticks and rocks clashed with police manning a perimeter outside the presidential compound. The police responded by firing tear gas.
In office since 2007, Correa has drawn increasing criticism over a constitutional reform package that would allow him to stand for re-election when his current term ends in 2017.
Indigenous protesters, who have been particularly vocal critics of Correa, blocked roads in six of Ecuador's 24 provinces Thursday, including the Pan-American Highway to Peru.
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But in a setback for protesters, transport, education and health services were all operating normally in the country's largest cities despite a call for a general strike.
A heavy police presence was on the streets in key cities, including 5,000 officers in Quito.
The 52-year-old Correa has been Ecuador's most popular president in decades, building hospitals, schools and roads and expanding social spending.