Any ship, or for that matter anything that floats, can go upriver. In the right conditions of course, which depended mostly on the depth and width of the vessel, and more importantly the depth and width of the river. What is important to stress out is there is no catch-all number that we can say „these types of ships could go X distance inland“. It depended from river to river, and ship to ship. Sometimes they could go all the way inland, sometimes they couldn't even enter it.

The ship also had to have a propulsion system that would allow it to counteract the flow of the river if it hoped to go upstream. Ships that could be oared would have an easier time, and while sail ships occasionally could even sail up the river, they would more usually be towed by smaller boats (their own, or the local ones) or even sometimes by animals, or even people, on the land nearby.

I like to demonstrate this concept with this image of Seville made in early 17th century. You can spot all sorts of vessels, including galleons (which were of the medium size of the time) that were used for Trans-Atlantic shipping. Yet Seville was about 80km / 50miles up the river of Guadalquivir from the coast!

Now to get to caravels. One of the features they are praised for was indeed their ability to go up rivers. What this usually means is that caravels, like other ships praised for this feature (norse longboats for example) had a great balance of handling well the open ocean and the rough seas and being small and nimble enough to go up smaller rivers. So, to answer your question, yes, the caravels could and regularly did go up the rivers.

To demonstrate this ability lets turn to primary sources. In 1450s an Italian Alvise Cadamosto (or Ca Da Mosto, or Cada Mosto. different spellings abound) joined Portuguese Infante Henrique (famous as Henry the Navigator) and took one of the formers caravels to the Senegambia region to trade (mostly they took slaves in exchange for horses). He left an account which was first printed in various exploration collections in the 16th century, and was subsequently translated to English in 19th century in Richard Kerr’s A General History and Collection of Voyages and Travels, Volume II from where I am taking the following excerpts.

Here is the description he gives of the river Senegal he received on the start of the voyage, that confirms that the Portuguese regularly sailed up and down the river, considerable length, as well as dangers that had to be looked after:

[Section IV] All ships that frequent the Senegal ought carefully to observe the course of the tides, the flux and reflux of which extend for seventy miles up the river, as I was informed by certain Portuguese, who had been a great way up this river with their caravels.

[Note, he says seventy miles, but will return to the word „miles“ later]

When the river looked too narrow for larger caravels, they sent smaller caravels, and then boats to see if it could be navigated. The small boats found the river deep enough but had other features that they deemed not suited for travel upriver so they gave up:

[Section VII] Next day, having but little wind, we sent on the small caravel before, well manned, with directions, as their ship was small and drew little water, that they were to proceed as far as possible up the river, observing whether there were any bar or sand banks at its mouth, and to take the soundings with great care; and if the river were found navigable, they were to return and make signals to that effect. Finding four fathoms water at the entrance, the caravel brought to, and made the concerted signal; on which it was thought proper, as that caravel was small, to send another boat well armed along with her up the river, and they were strictly enjoined, in case the natives were hostile, to enter into no conflict with them, but to return immediately to the other ships, as the object of our voyage was to cultivate friendship and trade with the country, which could only be accomplished by policy, not by force. The boats accordingly proceeded up the river for two miles, leaving the small caravel at anchor, and found the banks everywhere beautiful, with sixteen fathoms water. But as the river above this made several returns or reaches, they did not think it prudent to venture any higher.

To give an idea on exactly how far inland could the caravels go, here is a quote from the description of the sailing up the river Gambia, which estimates how far they traveled upriver:

[Section VIII]sailing up the river, we came to the place where Battimansa resided, which, in my opinion, was above forty miles from the mouth of the river. In going up the river, into which several lesser rivers fall, we sailed to the eastwards, and at the place where we came to anchor, we found it much narrower than at the mouth, being not above a mile in breadth, by our estimation[5]

The number appearing is „forty miles“ but the author of the English translation gives the following footnote for these sentences:

[5] According to our best maps or charts of the Gambia, this river is never less than four miles broad, and generally above five, till we get near 100 miles up the river, to the reach which encircles the Devils Point, where it still is two miles wide. It is possible that the original journal of Cada Mosto may have had leagues of three marine miles each, in which case the residence of Battimansa may have been at or near the Devils Point, above 100 miles up the river.--E.

And supposes that the it is possible that the values are supposed to be in Iberian leagues (of around 3 nautical miles, or 3.5 english miles) and somewhere the error occured in noting them as miles. The error, if it happened, could occur by Cadamosto himself, or in his manuscript and first printing of his work, or anywhere else. Without access to the original texts - and more likely even with them – and without other texts to crossreference we can't say for sure. I personally have already encountered a mistake that someone wrote miles instead of leagues, allthough that certainly doesn't mean it happened here.

All in all, caravels could and regularly did go up the rivers. How far depended on the river. One expedition reached either 40 or 100-120 miles inland. And the (larger) caravels wouldn't go after the river narrowed to less then 1 or 3.5 miles width.