The local museum in the town sadly doesnt seem to provide much information on this, thank you.
Tl; dr: As for the case of Ribe, I suppose Ribe River (Ribe å) was enough deep and wide for the ship traffic at least up to the High Middle Age, though it is difficult at least for me to specify any single factor among the different possible candidates, as shown below.
1: The draught (draft) of the Scandinavian boats and ships during the Viking Ages is enough shallow to sail into the river
The draught of Late Viking Age cargo ships salvaged from Roskilde Fjord is only around 1.0 meter deep (1 meter for ocean-going Skuldelev 1 and 0.9 meter for coastal Skuldelev 3, respectively linked to the description of individual ship remains in Viking Ship Museum, Roskilde, Denmark), and those of some battleships are even shallower. This is one of the strongest points in nautical/ ship-building technology of the Viking Age Scandinavia that enabled the Vikings to approach to careless targets.
Previous researches also classify Ribe as a inland [town] at navigable rivers (Englert 2015, after Andren and Bill), the same category of Odense in Fyn, so at least it was not until the 13th and 14th centuries (when the bigger cog ships became more and more popular around the Northern Seas) that waterways around Ribe became the bottleneck of the traffics.
2: Vikings certainly knew some elemental civil engineer works, though they didn't seem to invest some of their finest works into the harbor of Ribe.
Both in modern Denmark and in Norway, scholars have identified some archaeological sites of the artificial canals from Viking Age Scandinavia, possible to control the sea traffic in the strategical point:
I haven't heard similar remain found in Ribe, so I suppose the inhabitants made use of natural waterways.
(Added): As for dredging by the Vikings/ Medieval Scandinavians, I know only the 15th century regulation (fine for casting the ballast away into the harbor) from Medieval Denmark (Deggim 2005: 54-57), but their origin might be able to date further back into the Middle Ages (though no hard evidence at least in Scandinavia).
As for more details for this topic, the following thread might be interesting: When and where did the first major port or harbour dredging operations take place? What vessels and equipment were used?
3: The local museum in the town sadly doesn't seem to provide much information on this
They (at least their current exhibitions) suppose that the pier built in the river functioned as a main harbor for the Viking Age Ribe, supplanted by the land transport. Some of their short film feature this pier, probably reconstructed from the remains of the holes for piles of the piers:
References: