I know in poetry that a section with more than one line is called a stanza, but what is a single line on its own in poetry called?
The monostich is a stanza, or a whole poem, consisting of just one line.
A lines of poetry is sometimes called a stich (pronounced like "stick"), so a mono (meaning "one") stich (meaning "line"), is a "one-line".
Here is a clever monostich by A.R. Ammons, where the title plays just as much of a part as the rest of the poem:
Bravery runs in my family.
Praxis by Wendy Xu is a poem with stanzas in monostich:
I had put down in writing my fear of the war
I too pined for pastoral description
The blue of the water was the blue of the world
Newness does not, for me, equal satisfaction
A finite number of concentric rings I push out into space
A tedious fabric moving through time without malice
An act of oration, rebellion, inventory, fantasy
The sound of the earth closing its one good eye over me
Imagine: you reach out towards the margin’s white hand
You do what your poems want and are clean
When you lay down your thorns you will be done
You do not take up arms against anyone