Back in february 2006, a question was asked about the origin of OBJECTS OF VERTU on ebay's antiques discussion board.
Since no complete & satistyfing answer, written in english, could be found online, I decided to make a translation & synthesis from documents that could be found, written in French. Since english is not my native language, I do apologize for my syntax & orthography.

Here was the text I typed :

Tuscan (language from Tuscany, Italy)was the most notorious language, after latin, in pre-17th century Europe (before French took over it). It had its own dictionnary as soon as from 1607. This is due to the fact many famous authors were then Tuscan (Arioste, Petrarque, Arioste, Machiavel) but its universality was too due to the fact that the Florentins created the modern language of History and Art critic. During the 17th century, any educated French or French collector knew this Italian language.
The Italian language of the Arts used the word "virtù", widening its signification of will of good to the notion of beauty. Art writers from Tuscany used the Greek word dunamis (power) that the Latins had traduced by virtus, they understood this "virtu" word as the power to create shapes of an exceptionnal beauty. Was "virtuoso" the artist able to make masterpieces, but too the intellectual able to give such rare subjects and the collector able to appreciate either of them.

During the 17th century, "virtu" and "virtuoso" entered the european language of litterature & arts.
But they entered it first with their french translation. Why ? Mainly because of the influence of the Italian born Mary of Medici.
But this french translation had a short life, Richelieu and Colbert did everything possible in order to suppress the Italian influence. The first french dictionnary didn't show any entry for the words "vertu" and "vertueux".
Nevertheless, those words kept being used by a few "connaisseurs".

The Italian "vertù" had a better destiny in english, even until nowadays with the french "vertu", like when the terms "OBJECTS OF VERTU" are used (those terms appearing in the Oxford dictionary of English) : Strange example of a french word, used in its meaning of an Italian origin, still being used like a fosil in english but having disappeared in french except in the "frenglish" language of the art market.

Why this strange phenomenon ? The english habit of "Grand Tour" in Italy, with a long stay in Paris on the way back, answers for the most parts. The word "vertu" (french) appears in many english travel diaries from this era. Many of those travellers from the British aristocracy were bringing back multiple Art works with them, some of them even qualifying themselves of "vertueux" in consideration for the collection they had gathered.
Nevertheless, even in England, in the Art language, the use of the word "vertu" gets reduced during the 18th century. No more is it used to comment on a great artist or masterpiece (the french word "genie" for genious being rather used then). "Vertu" becomes a specialized word for artists and collectors, used to name a certain type of objects : the "objects of vertu".

What are those "objects of vertu" ? They include multiple categories of Art works : small or medium size, ... Their origin is usually Italian, Renaissance era. They are little masterpieces of technic and virtuosity made by top quality artists who, during the middle ages, devoted all their skills and know-how into making liturgical objects, enamelled plates of devotion, ... During the Renaissance, they were majolicas/ceramics decorated with non-religious figures or mythological scenes, small sculptures or bronze medals done in the Antique way, ....
The collection and gathering of those pieces show the personal "virtù" of the collector.

Another explanation for the english use of the french "vertu" word is because of the war of religions between catholics and protestants. Many high-end french makers of a calvinist origin settled in London and found a market of rich collectors interested in the "vertueux".

During the 18th century, "objects of vertu" was only used to name the greatest achievements in decorative arts (like little boxes for tobacco, and others boxes of an incredible perfection).
When the Goncourt brothers (french writers & historians, mid 19th century) reinstated the taste for Rococo, the english terms "objects of vertu" became widely used again : to name high end objects (like Faberge eggs, ...)