His wife, Amanda Kloots, said his health is going a little downhill, but didn't provide specific details.
Cordero, 41, initially went to the hospital on March 31 with what they thought was pneumonia, according to Kloots. He later tested positive for COVID-19 and was put in a medically induced coma to help his breathing.
He had to have his leg amputated because of issues with blood clotting.
On Instagram, his wife teared up while updating fans this week.
"I know that this virus is not going to get him down, that's not how his story ends, so just keep us in your thoughts and prayers," Kloots said.
Last week she updated fans that he was officially awake after spending weeks in a coma.
Cordero was nominated for a Tony in 2014 for his role in "Bullets Over Broadway."