Prisons Service spokesman Francis Enobore says the board also is suspending 11 officers while it investigates escapes from a third prison.
Jailbreaks are common in Nigeria, where prison guards are easily bribed. A new controller-general of prisons has promised to halt that.
Enobore said those dismissed include three senior officers at Kuje medium-security prison in Lagos, which houses many high-profile suspects in corruption cases being pursued by President Muhammadu Buhari's government. The jailbreak in June involved two men accused of kidnapping, raping and killing a woman.
In July, 13 inmates escaped from Koton Karfe prison in central Kogi state. Six have been hunted down and returned to prison.