The obligation to enforce fines is not self-evident from a verse that says, “if men argue…,” so let’s contextualize it. Verses 18-19 say that if two men quarrel and one then physically assaults the other so that he becomes bedridden, it’s not a capital offense. Rather, the one who perpetrated the act must pay his victim for lost wages and medical expenses. In total, there are five categories of fines that the courts can impose depending on the case: damages, pain, medical expenses, lost wages and embarrassment. (In Hebrew, these are nezek, tzaar, ripui, sheves and boshes, respectively.)
These fines can be imposed by an authorized court (beis din) for damage done by one person (or his property) to another person (or his property). As with capital punishments, these fines only apply in the time of a duly-ordained Sanhedrin.
The obligation for a court to impose fines in appropriate cases is discussed in the eighth chapter of the Talmudic tractate of Baba Kama. In the Shulchan Aruch, it’s in Choshen Mishpat 1. (Despite the fact that it is in the Shulchan Aruch, which typically only discusses mitzvos that we can perform today, there it specifies that these fines can only be imposed under the Sanhedrin system by properly-ordained experts.) This is #236 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.