[shwick]

I live in a non-smoking apartment building and someone in a surrounding apartment smokes and turns their bathroom fan on. The smoke then gets into my bathroom through the fan entrance.

Turning my fan on doesn't keep it out.

I tried taping the fan entrance in the ceiling with a couple layers of plastic wrap, but I can still smell it.

What material will block cigarette smoke?

[NicotineFiend]

My suggestion:

Place one of those Fabric Softener cloths you put in your laundry in front of the fan, attach a couple of them to it somehow, using tape or a sticky product that will keep it in place when the fan is on, by doing this, the smoke that comes out of the fan will go through the fabric, and it will kind of strain the smell, by the smoke entering out of the little wholes, the odor just might change.

Try it.
It will most likely work.