Dzhokhar Tsarnaev, 19, was in "very serious" condition at a Boston hospital after being captured Friday night, Menino told ABC's "This Week" program.
"And we don't know if we'll ever be able to question the individual," he said without elaborating.
Tsarnaev's brother, Tamerlan, 26, was killed in a firefight with police earlier on Friday as officers hunted them for the twin blasts on Monday that killed three and injured 176.
U.S. Senator Dan Coats, a member of the Intelligence Committee, said it was questionable whether Tsarnaev would be able to talk again.
"The information that we have is that there was a shot to the throat," Coats told the ABC program.
"It doesn't mean he can't communicate, but right now I think he's in a condition where we can't get any information from him at all," said Coats, an Indiana Republican.
(Reporting by Doina Chiacu and Susan Cornwell; Editing by Vicki Allen and Philip Barbara)
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