In a two year clinical trial for Tysabri (natalizumab) hair loss was not reported as a side effect.
Some other medications used for multiple sclerosis (MS) are known to have hair loss as a side effect including:

• Azathioprine
• Methotrexate
• Cyclophosphamide
• Some of the interferons eg. Avonex, Betaseron
• Gilenya

Other medications that may cause hair loss including:

• Antibiotics
• Antidepressants
• High blood pressure medications
• Hormone medications
• Birth control pills
• Mood stabilizers
• Steriods

Hair loss can also be related to other medical conditions:

• Autoimmune disorders
• Thyroid disease
• Hormonal imbalance
• Scalp conditions
• Childbirth
• Stress

If you find you are losing more hair than normal or are concerned about hair loss, it is important to discuss with your healthcare provider. If they determine the cause they are more likely to be able improve or resolve the issue.