Most of its tracks exemplify two of Montgomery's distinguishing techniques: "thumb picking" and the use of octaves.

In 2017, the album was selected for the National Recording Registry by the Library of Congress as "culturally, historically, or aesthetically significant".

[2][3] The album is considered by many fans and critics to be the pinnacle of Montgomery's recorded studio work.

[6] AllMusic critic Michael G. Nastos praised the album, writing: "Setting him apart from the rest, this recording established Montgomery as the most formidable modern guitarist of the era, and eventually its most influential...Montgomery is clearly talented beyond convention, consistently brilliant, and indeed incredible in the company of his sidemen, and this recording—an essential addition to every jazz guitarist fan's collection—put him on the map.

"[4] Of the CD reissue, critic Chris May of All About Jazz wrote: "The Incredible Jazz Guitar burst onto the US scene in 1960 like a benign hurricane, and it still sounds like a gale almost 50 years later... Montgomery—empathetically accompanied by pianist Tommy Flanagan, bassist Percy Heath (then riding high with the Modern Jazz Quartet), and drummer Albert Heath—makes the guitar sound like it never had before.