The 18-year-old appeared to land awkwardly while attempting to control a dropping ball shortly before the 41st minute and limped from the field with the help of two Chelsea physios and was replaced by Pedro Rodriguez.
Chelsea were ultimately held to a frustrating draw by Burnley as goals by N'Golo Kante and Gonzalo Higuain were cancelled out by strikes from Jeff Hendrick and Ashley Barnes, but Hudson-Odoi's injury could have much bigger implications.
"Really gutted to end my season with an Ruptured Achilles, gotta work hard and try and come back stronger for next season!!!" Hudson-Odoi posted on Twitter.
Really gutted to end my season with an Ruptured Achilles, gotta work hard and try and come back stronger for next season!!!😢🙏🏾❤️ pic.twitter.com/PXC53WszdH— Callum Hudson-Odoi (@Calteck10) April 22, 2019
Assuming postmatch media duties in place of Maurizio Sarri, Chelsea assistant Gianfranco Zola confirmed that the 18-year-old is set for a long absence.
"It's not an easy one," he said. "I think it's a serious injury. It's his Achilles tendon. I cannot tell you the extent of it. I don't know -- he'll have to have an examination, but it's not looking good."
Hudson-Odoi's injury adds a further layer of uncertainty to what was set to be a summer of intense speculation about his future.
Sources told ESPN FC as recently as last month that Hudson-Odoi remained intent on leaving Chelsea this summer, despite failing in his attempt to force through a January move to Bayern Munich with a formal transfer request.
Hudson-Odoi and his representatives have so far rebuffed Chelsea's attempts to re-open talks over an extension to his current contract, which expires in June 2020, but the prospect of months on the sidelines could force him to re-evaluate his options.
Chelsea also lost N'Golo Kante to injury at half-time against Burnley, but Zola does not expect the France international's problem to prove serious.
"N'Golo was taken down on the counter and, as he fell, he fell on the foot of a player, so he had a contusion in his ribs," Zola explained. "He couldn't breathe totally. He'll be alright [to face Manchester United on Sunday]."
Chelsea went into Monday's game knowing a win would greatly boost their chances of a top-four finish, following defeats for Tottenham, Manchester United and Arsenal over the weekend.
But instead Sarri's men were picked apart at set pieces by Burnley and frustrated by the visitors' deep defending and time-wasting.
"We tried everything to win the game," Chelsea defender David Luiz told Sky Sports. "It's difficult when you play against a team who have two chances and score two goals and didn't want to play the game.
"It's anti-football. Losing time [time wasting] all the time, especially when you have the ball. Their players went to the floor and stopped the game.
"They were playing 11 inside the box. It's difficult to score against a team like that."
Zola added: "There was too much time-wasting. We thought five minutes [added time] wasn't enough to compensate for the time-wasting. But we did everything we could. That's the reason we're frustrated."
Burnley coach Sean Dyche, whose team are near locks to avoid relegation after the hard-fought point, bristled at the "anti-football" suggestion and praised his players for withstanding Chelsea's pressure.
"There are nights like tonight when you just have to give everything, every inch," he said. "You know, it used to be a really good thing when fans see their team give everything. They used to love it and maybe it's still got a place."