Rada Abazovic succumbed to loss of blood in hospital after the raid on their family home in nearby Kozici village, near the eastern town of Rogatica, at 9.30am (0830 GMT), Veljko Maric, the director of the hospital in the nearby town of Foca, said.
Her 47-year-old husband Dragomir, who was wanted by a Sarajevo court over alleged atrocities committed in Rogatica during Bosnia's 1992-1995 war, suffered serious bullet wounds in Thursday's incident which Eufor said were self-inflicted.
Their son Dragoljub, 12, was also injured during the shootout, which began after the peacekeepers opened fire on the fugitive.
"Rada Abazovic, 46, died from the loss of blood after being shot in the stomach," Maric told AFP.
"The boy was operated (on) and his life is not in danger. His father sustained serious head wounds and his condition is still not stable," said Maric.
First reports wrong
Bosnian Serb police had initially reported that Abazovic was killed. But "first reports were wrong and the man is seriously wounded and is in critical condition", said police spokesman Radovan Pejic.
Eufor confirmed there was a shooting incident in the vicinity of Rogatica, some 60km east of Sarajevo.
"Eufor troops fired upon them and they returned fire. During the exchange two people in the house were injured. The suspect, unable to escape, subsequently injured himself," Eufor spokesman Jem Thomas said.
The 6300-strong Eufor, comprising troops from European Union countries, provides deterrence and continued compliance with provisions of the US-brokered Dayton accords which ended the war.