Yes, and no.

For a lot of people, the bike's stock saddle is a torture device. If you have any kind of distance to ride and the saddle doesn't fit, it will hurt. Also, if your body isn't used to biking, your body will hurt because it just isn't used to what you're asking of it. So yes, hurting is normal as part of *starting* to bike.

There are lots of saddles out there, including one that won't hurt you. Unfortunately, there's no easy way to figure out if a new saddle will suit you without trying it. As you bike more, your body gets used to the activity and hurts less. So it is not normal to *keep* hurting. And it can be tricky to figure out if the pain is that the saddle is wrong or that you're not used to it at first. So...

I would back off the distance a *lot* for a bit. Just go 1-2 miles at a time for about a week. That should be short enough that you have no real pain from the saddle. Then move up to a bit longer distance. If you've got a desk job, you should be up to your commute distance in a couple weeks. If your job is very active, you might want to be comfortable for a few more miles than your normal commute. That way if you have a rough day at work, you *know* you have the reserves to handle your commute. The extra practice will make handling traffic easier. And if you hurt on longer distances but not on short ones, it will be easier for you to tell if it's the saddle or the distance.