Cordero's wife, celebrity fitness instructor Amanda Kloots, announced the new development on Instagram Saturday.
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Cordero, 41, a Tony-nominated actor, initially went to the hospital in late March 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.
Kloots says blood thinners that were initially helping to ease some clotting in Cordero's leg began causing issues with his blood pressure.
"We took him off the blood thinners, but that again was going to cause the clotting in the right leg," Kloots said. "So the right leg will be amputated today."
The illness virtually snuck up on Cordero, the former star of "Bullets Over Broadway," who first just experienced fatigue, Kloots told "Good Morning America."
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"We were watching the news and we were trying to decide if this was the coronavirus," Kloots said. "It didn't seem like Nick had the symptoms. He just had this extreme fatigue. We just thought we'd ride it out. We'd see what happened and just isolate because all he wanted to do was sleep."
The couple has a son, 10-month-old Elvis Eduardo.
"The tipping point happened one morning. We were eating breakfast and I asked Nick to go change Elvis' diaper and I heard a huge thump," she said. "I ran into the bedroom and he had fainted."
Kloots said she sends her husband a daily home video so that a nurse can show it to him when he wakes up each morning.