"Really gutted to end my season with a ruptured Achilles," he wrote in an Instagram post. "Gotta work hard and try and come back stronger for next season!"
Due to the severity of the injury - which usually takes months to heal - Hudson-Odoi is set to miss England's Nations League semifinal against the Netherlands on June 6.
The 18-year-old clutched his right leg and fell to the ground after suffering the non-contact injury with minutes remaining in the first half. He tried to continue but soon signaled for a substitution.
It's a devastating setback for the Chelsea youngster, who finally earned manager Maurizio Sarri's trust after a frustrating spell in purgatory. Monday's match at Stamford Bridge had marked Hudson-Odoi's fourth consecutive Premier League start.
Bayern Munich reportedly submitted several bids for Hudson-Odoi during the January transfer window but Chelsea rejected each one. It's unclear whether the injury will affect his status as a transfer target this summer.
Hudson-Odoi's contract with the Blues expires in June 2020.