Hudson-Odoi limped off helped by two members of Chelsea's medical staff after sustaining the injury in the first half of the 2-2 draw at Stamford Bridge against Burnley.
The 18-year-old will miss the rest of the season as a result of the operation.
"Callum is seeing a specialist this afternoon and is expected to undergo surgery on his ruptured Achilles tendon this evening," said Chelsea in a statement.
Hudson-Odoi's injury is a major blow for Chelsea as they battle to qualify for next season's Champions League either by finishing in the Premier League's top four or winning the Europa League.
They are fourth in England's top division and face Eintracht Frankfurt in the Europa League semi-finals.
A product of Chelsea's academy system, Hudson-Odoi has also broken into the England team this year and his injury means he is likely to miss the Nations League semi-finals in June.