Interior Vice Minister Carlos Najjar says the miners are a bit dehydrated but in good health.
Najjar told Channel 6 state television more of the miners are expected to be rescued overnight.
He said the men are walking out of the mine on their own, being checked by paramedics waiting and taken to a clinic in the town of Bonanza.
Earlier, authorities said 20 of the 24 miners had been located and had communicated with rescuers at the El Comal mine in northern Nicaragua. The miners were trapped after collapsing earth blocked a shaft in the mine.