Hello.
We have portraits/statues of most influential people throughout history, we even have portraits (shitty ones) that date back to old egypt. But we don't have portraits of the most influential people of all. Why is that? And while we are at it, where did the blonde jesus depiction originate from?
I can speak for Jesus, but a good bit of this likely applies to Muhammed, as well.
First, Jesus was a peasant in rural Galilee. Many of his followers were illiterate, subsistence-level folk--not the kind of people commissioning portraits in the ancient world (or today). He died when he was really young (approximately age 33), apparently three years into his ministry (according to the gospel accounts). His extreme social marginality combined with his short life/ministry pretty much answers your question.
That said, a couple other things to consider. First, Jesus's followers apparently considered him divine in some sense. If they believed he was the Jewish God, traditional proscriptions of idolatry might stop them from making portraits of him. Also, in the Gospel of Mark (regarded as the earliest Gospel), Jesus's exalted messianic status is a secret kept to those from outside his inner circle. If this were actually the case, then most of Jesus's ordinary followers might have been seeing him as a typical rural rabbi or charismatic healer/exorcist, not someone you'd compare to the sorts of elite people who were portrayed in Ancient Roman portraiture.
How did he come to be seen as a blond (or a Chinese man, or a black man, or a Native American man)? Basically after almost all Christians were Gentiles in the Roman empire, they used existing conventions of Roman art to portray him. Thus, Jesus ends up looking like other figures in Roman art--philosophers, the "ram-bearer," Apollo, Dionysus, Jupiter, Orpheus and others. Later artists from other parts of the world did the same. For more detail and sources, I refer you to my earlier post on this topic:
In the case of Muhammad the situation is quite different than the humble, impoverished position in society of Jesus that /u/thepibbs alluded to. Muhammad was the founder and ruler of a state and head of a religion that was dominant in that state; quite obviously the most important person in his society.
Rather, portraiture simply didn't exist in Arabian society at that time. The earliest examples of Islamicate portraiture that I'm familiar with are the Roman-style frescoes in the Ummayad desert castles of Jordan/Syria that were produced a couple hundred years after Muhammad.
The earliest depictions of Muhammad by others were likewise centuries later. It's a disputed question but the earliest claim for such a depiction that I'm familiar with is on coinage, also in the Ummayad period.