At the end of July, 1783, Mozart took his wife Constanze to Salzburg to introduce her to his father Leopold and sister Nannerl, remaining there three months. During the course of the visit, Mozart composed two duos for violin and viola (the other being K. 424 in F flat), his only works for this combination. According to Constanze Mozart, both were composed on the behalf of Mozart's friend Michael Haydn, the underrated composer brother of Joseph Haydn. Michael Haydn had accepted commission from his (and Mozart's former) employer, the Archbishop of Salzburg, for a set of six duos, but fell ill after composing only four. Mozart, who respected Michael Haydn as a composer, stepped into the breach to allow his friend to meet his deadline. The grateful Haydn is said to have retained the manuscripts as a sacred relic.

Suggestions that Mozart deliberately imitated Haydn's style are perhaps somewhat fanciful. Mozart's interest in the unusual form prompted him to produce two masterpieces whose contrapuntal mastery and richness of texture clearly stem from the experience gained in the near-contemporary composition of the first three of the set of six string quartets dedicated to Joseph Haydn. Interestingly, Mozart did not completely relinquish these duos to Michael Haydn—in two letters sent to his father after returning home, he requests that the duos be sent to him in Vienna, along with the score of his opera Idomeneo.

Like its companion, K. 423 is cast in three movements, in this instance in the sequence Allegro, Adagio, Rondeau.

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