Apparently all other days of the week were named after Germanic words and deities. So why was Saturday, which was named after the Roman god Saturnus, the only exception? Why wasn't it called "day of Frey" or something, since Frey is a god of fertility just like Saturnus?
It is because there isn't an equivalent of Roman god Saturn in Norse mythology and Germanic tribes couldn't find a match so they retained the Latin origin Sāturnus.
OED says that Saturday is a word inherited from Germanic and modelled on a Latin lexical item. [classical Latin Sāturnus , the name of (the planet) Saturn + the Germanic base of day n., after classical Latin Sāturnī diēs day of (the planet) Saturn.]
Here are some further details from Wikipedia:
The Germanic peoples adapted the system introduced by the Romans but glossed their indigenous gods over the Roman deities in a process known as interpretatio germanica. In the case of Saturday, however, the Roman name was borrowed directly by Westgermanic peoples, apparently because none of the Germanic gods were considered to be counterparts of the Roman god Saturn. Otherwise Old Norse and Old High German did not borrow the name of the Roman god (Icelandic laugardagur, German Samstag).
On the other hand, there is another theory from Jacob Grimm that Saturday is named after Loki which is a figure in Norse mythology. (from Sæter - another name for Loki). However, this is not mentioned in modern dictionaries.
Here is an excerpt from norsemyth.org that includes the details of Grimm's theory:
Jacob Grimm, in his 1835 treatise Teutonic Mythology, gives a convoluted argument that Saturday is named for Loki. While the other days are clear translations from the Roman days of the week into their Germanic pagan equivalents, Saturday does not fit the pattern. Every other weekday is named for a god or goddess from the Norse mythology: Sunday/Sol, Monday/Mani, Tuesday/Tyr, Wednesday/Odin, Thursday/Thor, and Friday/Freya. Grimm asserts that the Saturday does not retain the name of the Roman Saturn, but is named for Sæter ("insidiator" or "one who lies in ambush"), a name that he connects with Loki and suports with Anglo-Saxon and Old Norse sources. However, there is no evidence of a historical Loki-cult, or that he was ever worshiped as a god. There are, instead, multiple contradictory portrayals of the slippery figure.
Note: The Scandinavian Lørdag/Lördag has no reference to either the Norse or the Roman pantheon; it derives from old Norse laugardagr, literally means "washing-day" or "bath-day". The roots lör, laugar and so forth are cognate to the English word lye, referring to detergent. In Icelandic, Saturday is Laugardagur and some argue it was Lokadagur (final day, Loki day).
According to Etymonline the Northern European Phaeton lacks the corresponding figure of Saturn, which, for that purpose was "borrowed" from the Romans:
seventh day of the week, Old English sæterdæg, sæternesdæg, literally "day of the planet Saturn," from Sæternes (genitive of Sætern; see Saturn) + Old English dæg (see day). Partial loan-translation of Latin Saturni dies "Saturn's day" (compare Dutch Zaterdag, Old Frisian Saterdi, Middle Low German Satersdach; Irish dia Sathuirn, Welsh dydd Sadwrn). The Latin word itself is a loan-translation of Greek kronou hemera, literally "the day of Cronus."
Unlike other English day names, no god substitution seems to have been attempted, perhaps because the northern European pantheon lacks a clear corresponding figure to Roman Saturn. A homely ancient Nordic custom, however, seems to be preserved in Old Norse laugardagr, Danish lørdag, Swedish lördag "Saturday," literally "bath day" (Old Norse laug "bath").
German Samstag (Old High German sambaztag) appears to be from a Greek *sambaton, a nasalized colloquial form of sabbaton "sabbath," also attested in Old Church Slavonic sabota, Polish sobota, Russian subbota, Hungarian szombat, French samedi.
In his book "The Seven Basic Plots" (ISBN: 978-1-4729-7618-5) Christopher Booker has a footnote (#19 p.623),
The central day of the Anglo-Saxon week was reserved for Woden, chief of the Germanic gods. "Woden's day (Wednesday) is flanked by those named after gods representing masculine values: "Tiw's day" (Tuesday) after the god of justice, law and order, and "Thor's day" (Thursday) after the god of thunder, battles and physical strength. On each side of them are days dedicated to female divinities, the Moon goddess (Monday) and Freya (Friday) commemorating the wife of Woden, representing the female attributes of love, beauty, marriage and care for the sick. The week ends on "Surtur's day", named after a god who, like his Roman equivalent Saturn, presided over the transition between endings and beginnings (which is why the Roman festival of the winter solstice, marking the transition from the old year to the new, was the Saturnalia). Surtur plays a similar role in Norse/Teutonic mythology (hence we shall see the crucial part he plays in the events of Ragnarok/Gottderdammerung, the end of the world). This Saturday marks the moment when the old week ends, followed by the resurrection of the "Sun" to mark the first day of the next (in Russian, Sunday is still named "resurrection day").
The Babylonians named the days of the week after planets as part of their system of astrology. The Romans and the Greeks borrowed heavily from this system as part of their astrology. It was not until Constantine the Great that the Roman Empire adopted the 7-day week for timekeeping purposes, and, when it did, the astrological names were retained. (This was a few years before the adoption of Christianity.) Germanic tribes who came in contact with the Roman Empire adopted the 7-day week by translating most of the Roman planet names. I don't know why they didn't have a translation for Saturn, and I don't think anyone has more than speculation about that, but the corresponding name may have been considered bad luck. (Or maybe they didn't have a name for it.)
The fact that these were also deity names was secondary to their original astrological function as planet names. The Church did not use the planet names for the days of the week but instead used the Latin equivalent of naming Sunday the Lord's day, Saturday Sabbath, and the interveining days Second Day, Third Day, etc. That system is still I use in modern Portuguese.