He began refusing food a day after his arrest and is now said to be close to death.
The Israeli military confirmed the appeal had been rejected in a statement, saying the administrative detention order would stand unchanged.
"The military court of appeal rejected Khader Adnan's appeal regarding the administrative detention order. The four months administrative detention order that was initially served will therefore remain in effect," it said.
The court's decision prompted a furious reaction from the Palestinian Authority, with prisoner affairs minister Issa Qaraqa saying the rejection of the appeal was tantamount to murder.
"This decision is premeditated murder," he told AFP.
"With this decision, Israel has decided to kill Khader Adnan. What it has been doing for the last 57 days is a crime against humanity as a result of its decision to arbitrarily detain him in administrative detention," he said.
Qaraqa also called for protests and hunger strikes on Wednesday across the Palestinian territories in solidarity with Adnan.
Palestinian officials have warned of massive demonstrations across the West Bank and Gaza if Adnan dies in Israeli custody.
Bulus, who was present at Ofer military court, said the presiding judge had decided that Adnan held the keys to his own welfare and was responsible for his own fate.
He vowed that Adnan's legal team would take the case to the Supreme Court.
Clashes broke out on Monday between young Palestinians and Israeli soldiers outside the Ofer military prison near Ramallah in the West Bank, witnesses said. Many Palestinians are held in the jail.
It was not immediately known if there were any casualties in the violence.
A lawyer from Palestinian prisoner rights group Addameer who visited Adnan at his hospital bed in the northern Israeli town of Safed earlier on Monday said his condition "continues to deteriorate," the group said in a Twitter posting.
Earlier this month, a military court ordered Adnan held in administrative detention for four months, though with his condition worsening he has spent most of the past six weeks in a string of Israeli hospitals.
His lawyers say he is being held with both legs and one arm shackled to his hospital bed.
On Sunday, a Palestinian source told AFP that high-level contacts with Israel were under way in a bid to avoid a situation in which Adnan might die in custody.
"From a medical point of view, between 57 and 75 days on hunger strike is when you start to have internal organ death, so Adnan has entered the period of extreme danger to his life," the source told AFP.
The Palestinian Authority has formally requested his release, the source added.
Adnan has now been been on hunger strike for 58 days -- longer than any Palestinian prisoner before him, and Israel is under increasing international pressure to resolve the situation by either charging him or freeing him.
He says Israel has no evidence against him, and accuses his interrogators of mistreating him, saying they made crude sexual comments about his wife and pulled his beard until his hair came out.
Israel has not made any public allegations against Adnan, a one-time spokesman for Islamic Jihad.
Under Israeli military law, a court can order an individual held without charge for up to six months at a time. Each renewal must be approved in a new court session, but the renewals theoretically continue indefinitely.