If you include early hand colored scenes, then it might be 1916 Joan the Woman.
Black and white silent feature with colored scenes (burning at the stake)
This was the first film to use the Handschiegl Color Process (billed as the "Wyckoff-DeMille Process") for certain scenes. This process is especially noticeable in the scene of Joan burning at the stake, the use of red and yellow gave this a heightened dramatic effect.
The process was invented for this feature and was used for further features through into the 1920s.
(With technicolor's second full-length color feature release in 1922, that color film process became very popular and the number of technicolor inserts or parts in black and white features increased dramatically after this, replacing the hand-colored processes)
The question is problematic because due to the laborious nature of early colourization processes and that of filming in color being in its infancy, filming in black and white, with colored parts or inserts, was actually incredibly common throughout the late teens, 1920s and 1930s. It's considered unusual today but at one point in early cinema, also coinciding with the introduction of other new technology like talkies, it was incredibly common.
Have a look at these for example:
With this list, you might note the earliest (hand) colored scenes are listed for The Passion Play (Vie et Passion du Christ), released in 1903; but I had not included this as it was never released as a single feature, only as a series of shorts.
In his book Silent Cinema: An Introduction, Paolo Cherchi Usai writes that about 85% of silent films featured at least some color tinting and toning. Tinted footage could be achieved by either using a chemical process after the scene was shot or by using pre-dyed film stock.
The worlds longest narrative film at the time of its release, the Australian 1906 feature, The Story of the Kelly Gang, contains a red tinted sequence for a house fire scene. This was not listed as a feature with color, however.