I read this in hardcover at a library sometime in the late 1980s or early 1990s.
I don't recall much more than what's in the title. I'm not certain that the entire future civilization was Islamic; it may have been multicultural.
The starship in the novel could reshape itself. The exterior was made of overlapping metal plates. I recall the description sounding like a pangolin's armor, but I don't recall if it was compared to a pangolin in the novel.
The individual universes were likened to bubbles along some higher dimension, and one of the major plot points may have been the protagonist figuring out how to travel from one to the next. The universes may have been hierarchical.
It wasn't any great literary masterpiece, but it's been gnawing at the back of my mind for 20 years that I can't remember who wrote this thing. Thanks!