Is There any way to Install Minecraft on a USB stick?
This should help, even though it's for the old launcher, it should work if you know how to edit profiles in the new launcher. I don't think there's a way to convert a launcher profile to a file that you can use on a USB drive, but it should work.
If you're using the USB on a different OS from what you installed Minecraft on, you MAY have trouble running the game, but I'm not too sure about the inner-workings of the launcher and the game. This also applies to the launcher, but you should be able to just download the launcher from minecraft.net/download.