Media had earlier reported he had a suspected broken little finger on his left hand but England now say it is his right hand but will not confirm if it is broken.
Right-arm paceman Anderson is now doubtful for England's opening World Cup Group C clash with New Zealand on Friday. He was battling with three others for the two seam bowling spots in the lineup.
The 24-year-old sustained the injury during training and was immediately taken for further examination at a local hospital.
Anderson has only just recovered from a back problem which forced him out of England's recent victorious tri-series campaign in Australia.
Vaughany confident of fitness for WC: England captain Michael Vaughan said on Wednesday he hoped to play a full part in England's opening World Cup Group C match with New Zealand on Friday.
The 32-year-old has been working his way back to full fitness after knee and hamstring injuries but only fielded for part of the warm-up games with Bermuda and Australia last week.
"Hopefully I'll prove on Friday that I can get through a game," Vaughan told reporters.
"I've trained every single day and I've had nothing go wrong with the hamstring and nothing go wrong with the knee and I'm just looking forward to playing cricket now.
"There is absolutely nothing to suggest I won't play a full part in this World Cup."