If this is the first time a garnishment has happened, your employer cannot fire you solely on that basis. Title III of the Consumer Credit Protection Act (CCPA) prohibits an employer from discharging an employee because his or her earnings have been subject to garnishment for any one debt, regardless of the number of levies made or proceedings brought to collect it. Title III does not, however, protect an employee from discharge if the employee's earnings have been subject to garnishment for a second or subsequent debt. Also, the CCPA does not prevent your employer from firing you for other reasons: however, the termination cannot be based solely on the garnishment.
Some states have their own laws on wage garnishment. If a state wage garnishment law differs from Title III, the employer must observe the law prohibiting the discharge of an employee because his or her earnings have been subject to garnishment for more than one debt (as opposed to the single debt protection offered under federal law).
If you still have questions about your state's laws relating to wage garnishment, then you may wish to contact the agency in your state which handles wage and hour/labor standards violations, listed on our site's state government agencies page, or an attorney familiar with this area of the law.