The accident happened on the cross country course at Ballindenisk. Rodgers' horse Kilcoltrim Brigade was not injured in the incident.
Rodgers, 41, was an experienced and successful rider, and had been involved in many aspects of equestrian sport in Ireland during the last 10 years.
Eventing Ireland and the Fell Family, organisers of the Ballindenisk ODE, have expressed their deep sadness and shock.
Eventing Ireland Chairman John Wright said yesterday from Ballindenisk: "We are in a state of shock, which we are sure will be shared by everyone in the horse sport community. Karen was a well-known and popular figure in equestrian circles, and we wish to extend our profound and heartfelt sympathy to all her family and friends."
A full investigation is now being carried out into the circumstances of the accident.
Several deaths and serious injuries have marred eventing in recent years. British rider Eleanor Brennan was among nine riders killed during eventing competition in 2007. Other riders killed in 2007 included Amelie Cohen, Julie Silly, Jo-Anne Williams, and Maia Boutanos.
In March, US rider Darren Chiacchia suffered critical injuries during a cross-country event. After spending two weeks in intensive care, he is now undergoing rehabilitation.