I write fiction as well as poetry. And many a times I use poetry as a tool to bring out that acute feeling of pain or love (as required) in my explanations. What if I use poetry to introduce or end a scene? Is it alright to do so, or does it also has some damaging effect?
I've read several books where chapters are introduced by a poem. I do not see a problem with that.
If you choose a more disruptive approach, like putting the poem between scenes (or within one scene), you generate a "damaging" effect. Many readers will be puzzled, you tear them out of your story and normally a writer tries to avoid exactly that.
But breaking a rule is not automatically a bad thing. If you want to do it, try it. I would probably not read it, but I could imagine that there is an audience which like this experiment.
The worst thing that could happen is that I'm wrong and no-one likes it. Then you have failed and failing is good, because you can learn from it. Experience is such a valuable thing, so go for it.
As an example, The Malazan Book of the Fallen series by Steven Erikson opens every chapter with either a poem, or a snippet from an academic work from his fantasy world (mainly poetry, though).
My experience with this work is that, while I find the story amazing, I'm largely indifferent to the poems, and find myself often skipping them. They're often a distraction at best, or self-indulgence at worst.
This is not because I'm against poetry, it's just that they seem to have little or no bearing on the actual story itself. If you take the poems away, the story doesn't suffer. You don't miss out on some vital info. True, they do add a certain degree of richness and authenticity to the fantasy world, but for the most part, I couldn't see the point, and I honestly felt the books would be better without them, since they often break the flow of the narrative.
The point to be made is this: don't just insert the poems because you like poetry. Ask yourself what purpose your poems serve. Can the story live without them? Are they integral to the story? Do they fit in with your narrator, or your characters (i.e. who is telling the poem, and why)?
If you feel you still want poetry in your work, then I definitely suggest starting each chapter with the poem. This means people like me could skip it (if we don't feel like reading poetry), and it doesn't break the flow of the story too much by appearing in the middle of a chapter.
One of your characters could "write" the poem and recite it to another. You could present the poem as something in a book which a character reads, or establish that your character is a poet who is always composing in her head and tends to think in verse, so the poetry is actually coming from her thoughts.
But to stop dead in the middle of prose narration, insert a poem, and continue merrily along is disruptive to the flow of reading. Unless you're writing something truly surreal, where you're playing with the medium as part of how you're telling the story, I don't recommend it.
Poetry in a novel is dangerous because it backfires easily if it's bad, and (not to say anything at all about you) it's often bad. Or at least not good. Or just plain puzzling, like it's been put there just because it's Significant and the reader doesn't know why it matters that it's poetry. If the poem isn't good enough to stand on its own, the reader will be right to reject it. Jo Walton had a nice snark in the first post of her Rothfuss reread:
Apart from being that rare thing in fantasy, actually good poetry...
You have to be careful not to end up as one of her many targets.