This is not the case. Nowhere does Canon Law prohibit a cleric for working a job for money. In fact, Canon 139 (1917 Code) lays out certain professions that clerics either cannot engage in at all (secular notaries, being one) or they need an indult for (surgery and medicine). Simply because the SSPX requires some oath against this before tonsure does not make it "canon law". That is just something the SSPX does.
There was also the worker priest movement in France in the 1950s, that had some problems, yes, but was eventually allowed to continue in a certain form. There are still Novus Ordo priests in France that belong to this original movement. Not to mention, a large amount of Eastern Catholic priests also work secular jobs.
There are priests that are also taxi drivers, bus drivers for disabled children, network engineers, high school teachers, antique dealers, college professors, etc. Some chapels are in between being too small to support a priest full time but at the same time have a large enough group of faithful to need a priest close by and have Mass regularly. Some of these "worker priests" are able to fulfill this role, and these priests take no money for their priestly ministry. In fact, many of them put quite a bit of their own money into these chapels.
I questioned this also in my mind when it was posted. I can especially see with Traditional priests that they may work at a chapel that's too small to support them and where they might have to take on some work to pay the bills, get health insurance, etc.