The The family is worried because their son, Nnamdi Kanu, is very sick while in the custody of the Department of State Services.
They say Kanu urgently needs a heart specialist and they want President Bola Tinubu to make sure he doesn't die in the DSS custody.
Kanu has been in custody since 2021 after being brought to the country from Kenya.
His request for bail, based on his worsening health condition, was rejected by Justice Binta Nyako on Tuesday.
In a statement on Saturday, Kanu's younger brother, Emmanuel, said he was told earlier that his brother was very unwell.
He said Kanu needs immediate medical attention to prevent a serious health crisis.
The statement said, "We were informed this morning that he is very unwell. He has not been allowed to see his own doctors, and he urgently needs a heart specialist. He should not be left to die in DSS custody."
The family had previously criticized the political leaders in the South-East for not intervening with the President to help get their son released.
They claimed that some people were benefiting from his continued imprisonment, which is why the political leaders seemed indifferent about asking the President to release him.
The family said, "It's disgraceful that Kanu is being punished for advocating for the freedom of Ndigbo, and the leaders have deserted him to die in DSS custody."