The eye of Hurricane Matthew entered Cuban territory at 6.07 p.m. local time in Guantanamo province, battering the region with strong winds and heavy rain.
"The northern eyewall of extremely dangerous Hurricane Matthew is already pounding the eastern tip of Cuba," Xinhua news agency quoted Miami-based National Hurricane Centre (NHC).
Cuban President Raul Castro personally inspected storm preparations in eastern Cuba earlier in the day.
The category four hurricane, which can pack winds between 209 and 251 km per hour, is forecast to dump as much as 200 to 300 mm of rain and cause flooding along the island's southeastern coast.
More than 4,30,000 people have been evacuated from coastal areas prone to flooding, with the eastern provinces of Guantanamo, Santiago, Holguin, Granma and Camaguey under a hurricane warning since Monday.
In Guantanamo, which appears to be the most affected by Matthew, roads are blocked by debris or flooding, as 3 to 5 metre waves pounded the shoreline.
Flights, trains and bus transport from Havana and other parts of country to the eastern provinces have been suspended until the hurricane passes.
Hurricane Matthew earlier barreled through western Haiti, killing at least three people and displacing nearly 9,000.
Matthew is expected to turn north-northwest by Wednesday, heading to the Bahamas and the east coast of the United States.