Sako limped off in the first half of Palace's 1-1 Premier League draw at West Ham United on Tuesday.
Hodgson said the 29-year-old, who has scored six goals in all competitions this season, suffered damage to his ankle ligaments and remains a doubt to be fit for the start of the 2018-19 campaign.
"Baky's injury is a very serious one. He's fractured his ankle and damaged ligaments around it," the former England manager told reporters.
'People don't care enough about racism' - Aluko explains decision to delete her Twitter
"He certainly won't play again this season and may be a doubt to be fit for the start of next."
Hodgson described the type of injuries to hit his squad this season as "unusual" as he has just 19 players to choose from for Sunday's league fixture against Newcastle United.
"Our injury situation is unusual. A lot of clubs can get a number of muscle injuries, but we're in a situation where we've lost five for the season," he said.
"(Christian) Benteke, (Wilfried) Zaha, and (Mamadou) Sakho all spent at least 6 weeks out earlier in the season."
Hodgson added that Norwegian new signing Alexander Sorloth will replace Sako in the squad at Selhurst Park this weekend.
From pariah to hero, Sterling a Ballon d’Or contender and national treasure
Vieira announced as Crystal Palace manager