Clinton, 65, was admitted to New York-Presbyterian Hospital on Sunday after doctors discovered a blood clot related to the concussion she suffered last month after she fainted and fell down while recovering from a stomach infection.
She is being treated with blood thinners to help dissolve the clot, which is located in a vein behind her right ear that helps carry blood away from the brain.
Chelsea thanked the public via Twitter for their support while her mother is admitted to hospital.
'Thank you to all for sending good thoughts my Mom's way,' she tweeted yesterday. 'Grateful to all her doctors & that she'll make a full recovery!'
'Wishing all a healthy & happy 2013,' Chelsea tweeted. 'Grateful to be starting the new year with my family.'
Chelsea was also photographed with her face full of anguish as she left the hospital after visiting her ailing mother.
Hillary Clinton's husband and former President Bill Clinton has been spotted driving to and from the hospital in Washington Heights for much of the past 48 hours, US media reports said.
In a statement yesterday, doctors assured it was not a life-threatening condition and assured Clinton had suffered no brain damage or stroke.
"In all other aspects of her recovery, the Secretary is making excellent progress and we are confident she will make a full recovery. She is in good spirits, engaging with her doctors, her family, and her staff,' Drs Lisa Bardack and Gigi El-Bayoumi said in a statement.
