This was easier than I thought, but if anyone else has a need for this here is the code:

import org.newdawn.slick.Font;
 import org.newdawn.slick.geom.Rectangle;
 import org.newdawn.slick.geom.ShapeRenderer;
 
 public class TextBox {
 
     private float x;
     private float y;
     private float width;
     private String text;
     private Font font;
     private Rectangle rectangle;
 
     private String drawText;
 
     public TextBox(float x, float y, float width, String text, Font font, float margin)
     {
         this.x = x;
         this.y = y;
         this.width = width;
         this.text = text;
         this.font = font;
 
         // Break the text into words
         String[] wordArray = text.split(" ");
         drawText = "";
         String curText = "";
         for (int i = 0; i < wordArray.length; i++)
         {    
             if (font.getWidth(curText + " " + wordArray[i]) > width)
             {
                 drawText += "\n";
                 curText = "";
             }
 
             drawText += wordArray[i] + " ";        
             curText += wordArray[i] + " ";
         }    
 
         rectangle = new Rectangle(x-margin, y-margin, width + (margin * 2), font.getHeight(drawText) + (margin * 2));
     }
 
     public void draw()
     {
         font.drawString(x, y, drawText);
         ShapeRenderer.draw(rectangle);
     }
 }

Edit: There was a bug in the code that I fixed above. I guess it wasn’t so easy after all…