Melissa, who starred in the reality series Joan & Melissa: Joan Knows Best with her mother and competed against Joan on The Celebrity Apprentice's second season in 2009, released an update on her mother's status on Friday.
"My mother would be so touched by the tributes and prayers that we have received from around the world," Melissa said in the statement.
"Her condition remains serious but she is receiving the best treatment and care possible. We ask that you continue to keep her in your thoughts as we pray for her recovery."
Joan went into cardiac and respiratory arrest while undergoing vocal cord surgery at a New York City medical practice on Thursday morning, according to NBC News, and it is unclear how long she went without breathing.
She was then rushed to nearby Mount Sinai Hospital by ambulance, where doctors reportedly eventually placed her in a medically-induced coma.
Joan, who won The Celebrity Apprentice's second season, apparently performed a stand-up comedy routine for a sold-out crowd in Manhattan just 12 hours before the medical incident.