"byte: addressable unit of data storage large enough to hold any member of the basic character set of the execution environment"
Hence why the type that corresponds to it is "char"! Beyond that, the only thing that kinda sorta implies that it's the smallest addressable unit is the definition of CHAR_BIT:
"number of bits for smallest object that is not a bit-field (byte)"
This might be why the code space alphabet is defined by the standard so it will at least put an emphasis on 8 bits == 1 byte.
The question, though, was about whether it's the minimum addressable unit of memory. In the C memory model, it is, but by implication - you can't have two pointers that compare non-equal, but differ by less than 1, so a type with sizeof==1 is by definition the smallest you can uniquely address. However, the C memory model doesn't have to reflect the underlying hardware architecture.
The CPU itself used 32-bit addresses to access machine words, the size of which was determined by what was being accessed. External memory was limited to 32-bit. Internal memory had regions that could be 32-bit, 40-bit, or 48-bit. An address increment of 1 would thus move by that many bits.
Mercury Computer Systems shipped a byte-oriented port of gcc. Pointers to char and short were rotated and XORed as needed to reduce incompatibility. Pointers to larger objects were in the hardware format. This allowed a high degree of compatibility with ordinary software while still running efficiently when working with the larger objects. There was also a 64-bit double, unlike the 32-bit one in the other compiler. Data structures were all compatible with PowerPC and i860, allowing heterogeneous shared memory multiprocessor systems.