The 28-year-old sustained his injury while scoring 64 from 44 balls against the Tigers in Cardiff and did not field in the second innings, with Jonny Bairstow taking the wicketkeeping gloves in England's 106-run victory.
Vice-captain Buttler is expected to train with the squad on Wednesday and then be reassessed before England take on West Indies at The Hampshire Bowl on Friday, live on Sky Sports Cricket World Cup from 10am.
An ECB statement read: "Jos sustained heavy bruising on his right hip during the match against Bangladesh at Cardiff. He is responding well to treatment and will be reassessed later this week.
"We anticipate he will train with the rest of the squad at the Hampshire Bowl on Wednesday ahead of the match against West Indies on Friday."
Sky Sports Cricket expert Nasser Hussain said: "There are certain players England can replace but Buttler is irreplaceable - one of the great players in world one-day cricket.
"He looked like he was really struggling but luckily for England they don't play until Friday, it is a reasonably long break."
England captain Eoin Morgan suggested after the victory over Bangladesh that the chances of playing Buttler as a specialist batsman were slim, believing his hip may be easier to manage behind the stumps.
"It depends on the risk of him making his injury worse in the field. In theory, the best place to be would be with the gloves on," said Morgan.
"The worry then would be that the high catch went up and, with the gloves, he would have to take the responsibility to take the catch, and make his hip worse.
"We'll use every day as much as we can to try to get him back on the park. If he is a risk going into the next game, it might not be worth it."
You can watch every match of the 2019 ICC Cricket World Cup on Sky Sports Cricket World Cup (channel 404), including England's next game against West Indies from 10am on Friday.