All songs written by Wade Schuman except as noted Cicada received positive reviews from critics.

Calling it "a brave and unexpected record", he was complimentary of several tracks but singled out the collaborations with Gangbé Brass Band, Natalie Merchant, and the Kronos Quartet as highlights.

[1] In another four-star review, All About Jazz praised the band's eclectic makeup and concluded, "Even if Cicada doesn't surpass the novelty or the awards of the group's debut, Bahamut, it is a CD of spectacular aural aurora; one that brings an authentic, multi-referenced, American approach to the concept of world music.

"[2] Bill Lupoletti, host of the "Global a Go-Go" program on WRIR public radio, called Cicada a "brilliant album", highlighting "Child of a Blind Man", "I've Been Lonely for So Long", "Walking Stick", "So Glad", and "Dead Crow" as the album's best tracks.

[3] Allmusic's William Ruhlmann considered Cicada more "traditional jazz" than Bahamut, while still calling the band's sound "an eclectic mixture of roots styles that is nearly beyond category".