Blair has not specified exactly what the treatment entails but hair loss appears to be the side effect of the treatment she is undergoing.
"Today is a banner day," Blair wrote in the post which shows her posing with her support bike.
"I am being discharged from the care of an incredible team of nurses and techs and a visionary Dr. who believes in my healing as much as I do. This has been a process. And will continue to be one. I am immunocompromised for next three months at least. So no kisses please. I wanted to make sure all complications here were my private space. And we got through brilliantly."
Blair said she will go into details about her journey to recovery "when I am ready."
She has previously described suffering from pain and facial paralysis.
In a cover story for People magazine she opened up about her suffering, saying she has experienced "constant weakness and fatigue" and spasmodic symptoms which compromise her control over her face and voice.
However, she told the magazine she had some milestones to celebrate including her supportive followers on social media and the resilient support of her family.
Her son Arthur doesn't see his mum's challenges as weakness, but instead says, "Mommy's not sick. Mommy's brave," Blair said.