In a typical scalar in-order issue microcontroller, the instruction register holds however many bits are needed to control the data path.
Modern microcontrollers are typically Harvard architectures, with program memory stored in flash, with a modest amount of data/read-write memory on-chip. This means that, unlike traditional scalar CPUs, the bus width of program memory and the bus width of data memory does not have to be the same.
Microcontroller instruction sets are typically designed so that the instruction as a whole can be understood from the first word fetched from flash. Any additional words contain data only, and hence do not need to participate in instruction decoding.
As an example, here is the AVR block diagram from a data sheet that I picked at random:
The instruction register holds whatever comes out of program memory. Since AVR has 16-bit instructions, we would expect it to be a 16-bit register.
Now consider the PIC instruction set. Different models have different instruction sizes, anything from 12 bit to 16 bit. Modern microcontrollers can handle this just fine because, as noted earlier, instruction memory can have a different word size from data memory. This instruction word contains all of the information needed to understand what the instruction needs to do, so this is the size of the instruction register.
A mid-range core PIC has a 14-bit instruction word, so it will almost certainly have a 14-bit instruction register. And if you look at a data sheet, this turns out to be correct, and is even labelled on the diagram:
So in summary: On a typical modern microcontroller, the IR size is one word of program memory, and the instruction encoding is carefully designed so that this word contains all the information that instruction decoding needs.