You CAN put a shower curtain in the washing machine.
More Info: It does not matter if your shower curtain is vinyl, plastic or fabric, you can wash it in the washing machine. The best plan is to add a 1/2 cup baking soda to your regular detergent in the wash and one or two towels to provide some friction. During the rinse cycle, add a 1/2 cup of vinegar. Once the shower curtain finishes washing, you can hang it right back up to dry. Of course, before washing, you should check your particular shower curtain for any tags that may have specific instructions. A high quality shower curtain will be the easiest to wash.
Deter Mold and Mildew
Remember to always close the shower curtain after using the shower. This allows the shower curtain to spread out and dry quickly and consistently. A wet shower curtain leads to mold and mildew. Another quick way to avoid mold and mildew is to give a quick wipe down to both the shower and the curtain after each use. A squeegee left in the shower is great for this. There are also a number of sprays on the market that you can use to help keep your shower curtain clean.