Tsarnaev, 19, was captured Friday in Watertown, Mass., on the fifth day of a manhunt for whoever planted two bombs that exploded Monday near the marathon finish line, killing three people and injuring 170.
He was being treated Saturday at Beth Israel Deaconess Medical Center in Boston, where he was under police guard as investigators considered which charges to file, CNN reported.
Tsarnaev and his brother, Tamerlan Tsarnaev, 26 -- who was killed in a shootout with police Thursday night -- were suspects in the killing of a Massachusetts Institute of Technology police officer, in addition to the bombing attack at the marathon.
Dzhokar Tsarnaev could face state murder charges as well.
CNN legal analyst Jeffrey Toobin said under normal circumstances Dzhokar Tsarnaev would be arraigned Monday.
Typically, a suspect will be assigned a lawyer during the arraignment and the lawyer would request bail but Toobin said Dzhokar Tsarnaev "obviously" will not get bail.
"They will set a preliminary hearing that could happen in the next 30 days," Toobin said. "He will be indicted with the grand jury. And that's when the case will begin."
President Barack Obama said Friday night he has directed federal law enforcement agencies "to continue to deploy all the necessary resources to support the investigation, to collect intelligence, and to protect our citizens."
"We will determine what happened," the president said. "We will investigate any associations that these terrorists may have had. And we'll continue to do whatever we have to do to keep our people safe."
Obama said "many unanswered questions remain."
"Among them, why did young men who grew up and studied here, as part of our communities and our country, resort to such violence? How did they plan and carry out these attacks, and did they receive any help? The families of those killed so senselessly deserve answers," the president said. "The wounded, some of whom now have to learn how to stand and walk and live again, deserve answers."