I don't want to rain on your parade but if your hybrid has disc brakes front and rear, chance are that you have vertical dropouts.

For fixed gear, you'll need a magic-gear, perfect gear where you will have no slack in the chain since your dropouts don't allow you to adjust chain tension. Once the chain begins to wear out and 'stretch' you will run into problems.

Another option is to go single-speed and use a tensioner.