No home requires insurance. It is not legally mandated, as it is with car insurance. But without it, you’ll have to cover major damages and liability claims and lawsuits out of pocket. 
A prefabricated home, also known as a prefab or modular home, is regarded by insurers and lenders much like any other home. It may not have been built on the premises and it may have been cheaper than a conventional home. But the big differences end there. A modular home and a conventional home have more in common than not. They both will be built to code, they're both permanent structures, and they're both easier than a trailer home (or manufactured home) to customize.
With that in mind, it stands to reason that a prefabricated home is subject to all the same insurance considerations as a site-built home:
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Once your mortgage is paid off, home insurance can be bought or canceled at your discretion.
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Modular homes are covered under standard home insurance policies. So, you don't need to look for a specialty provider.
Mobile, trailer and manufactured homes are another story entirely. Some people will use prefab and manufactured interchangeably, but they're two completely different categories. A modular home is shipped in pieces and assembled on site. It’s usually much larger than a trailer home, and it will not require any special insurance. In fact, your insurer probably won't even bother to ask if your home was prefab or built-on-site.
Just make sure, when buying insurance, you correctly identify your home as either prefab or manufactured to ensure that you're getting the right policy for your home.