Tsarnaev's attorneys had requested the evidence so they could prepare to oppose a potential death sentence, The Boston Globe reported Wednesday.
In denying the defense request, U.S. District Judge George A. O'Toole Jr. said the attorneys had not made "a prima facie showing of materiality."
Prosecutors told the judge they had already turned over all evidence required of them to Tsarnaev's attorneys. They added they were under no obligation to turn over information that might help in a death penalty presentation.
The judge ruled prosecutors could be required to turn over such documents, but defense attorneys had failed to prove the information they wanted was relevant.
"[The defendant] essentially seeks access to the government's information haystack because he is confident there are useful evidentiary needles to be found there," O'Toole ruled. "That is simply not enough to trigger a disclosure obligation."
The defense successfully argued for the release of recordings of Tsarnaev's phone calls from jail, saying transcripts they had received did not convey information such as vocal inflections.
Tsarnaev, 20, faces multiple charges that could result in the death penalty for the April 15 bombings in which three people were killed and more than 260 injured.