What is the musical setting of a German poem for solo voice and piano called?

The musical setting of a German poem for solo voice and piano is known as a Lied. This term specifically refers to the combination of vocal music and poetic text that is typically composed for voice and piano, embodying characteristics of romantic expressiveness and lyrical melody. The tradition of the Lied includes notable composers such as Franz Schubert and Robert Schumann, who elevated this form by marrying profound emotional depth in the music with the poetic imagery of the lyrics.

While the term 'art song' can refer to similar settings in various languages and cultures, it is more general and not specific to the German-language tradition. Scherzo generally indicates a lively, playful type of composition, often found in the classical symphonic repertoire. Ballade typically refers to a narrative, often evocative piece that can be instrumental or vocal but does not specifically denote the German Lied form. Thus, 'Lied' is the precise term that captures both the cultural and musical context described in the question.