Musically, "(I'm Your) Hoochie Coochie Man" is a signature template for the Chicago blues style. And there are a few elements that became key to the style and remain prominent in blues today.
The Lineup
The lineup on the 1954 recording consists of a strong harmonica playing lead, an electric guitar, a piano, and a simple rhythm section held down by a bass and a drum kit. This five-piece line-up would become a classic blues line-up, in part because of Muddy Waters and Chess Records.
Stop-Time
Stop-time is that classic blues sound where the beat and instrumentation stops on the first beat in a measure, leaving a pause before a brief build to the next downbeat and giving the impression of a complete stop in the song.
At the very start of "Hoochie Coochie Man," which is in 4/4 time, a snare comes in on the third beat in a measure, the guitar and harmonica hit hard on the fourth and first beat, and stop time commences, accented by Muddy's powerful singing through the pauses. We don't need to hear more than a measure to know that we're hearing the blues.
Blue Notes
A blue note, or a "worried note," is a classic feature of both jazz and blues in which (incredibly skilled) singers hit notes a tiny bit flat. In other words, they "bend" the tones beyond the usual 12-note scale to give a worried feel to the songs (which, like "Hoochie Coochie Man," are often in major keys).
Muddy Waters sings the blue notes in this song so effortlessly that it sounds decidedly casual and natural. Listen, for example, to the final note in the line "I got a black cat bone." Muddy falls flat on "bone," but instead of sounding out of tune, it sounds beautiful and distinctively blues-y. That effortless feel to the singing is actually no simple feat.