The two items are estimated to be worth £6m, and are considered some of the most important artefacts from the US civil rights movement. The American President Barack Obama was sworn in for his second term using the Bible.
King Jr's daughter, Bernice, wants to keep the objects within the family, however it's reported her brothers, Martin Luther King III and Dexter Scott King, want to sell them.
Ms King was made to give the Bible and medal to court in Atlanta until an ongoing legal case over them was finished.
She said she was "utterly appalled and ashamed" her brothers wanted to sell the items, which she called "sacred".
"These items should never be sold to any person... or any institution.
"I take this strong position for my father because Daddy is not here to say himself, 'My Bible and medals are never to be sold'."
The judge is specifically ruling whether the Bible and medal should go to the two brothers, who control the Martin Luther King Jr estate, or go to a full trial.
Estate lawyers have not commented on the case.
Martin Luther King Jr won the Nobel Peace Prize in 1964.
He's widely praised as one of the central figures to help end racial segregation in America.
