I remember a Popular Mechanics cover that indicated that soon, Nuclear reactors would be powering houses and even cars. I don't believe there's a practical limitation that means that a ship has to be huge to be nuclear powered. The limiting factor on cargo ship size is the Panama Canal; there's even a name for it, "Panamax."
(Note, there are ships that are larger (Post-Panamax), as well as Suezmax but they are obviously limited in use and less common)
Nuclear reactors per se can be made pretty small, e.g. research reactors typically have a maximum (steady state) power output of a few hundred kW (roughly a car engine). OTOH the minimum economic size is probably somewhat larger.
I would imagine there's similar issues as with nuclear power plants on land, that is, to get the best return on the invested capital you want to run them with as high capacity factor as possible. So some short-range ship that spends a large fraction of its time in port is probably a poor match, whereas a trans-oceanic liner with quick turnarounds, like a container ship, could make for a good fit.
Nowadays there's "New Panamax", after a new set of locks opened in 2016 enabling (much) bigger ships.
One thing to consider - you could oversize the reactor and have grid hookups available in the harbor so that these ships can provide generation capacity while they are just sitting around. While they are out at sea, the nuclear reactor system could have a secondary mode that is more efficient/safe/etc for seafaring operations.
(Note, there are ships that are larger (Post-Panamax), as well as Suezmax but they are obviously limited in use and less common)