Among almost 9,000 children aged 10, those who had been bottle fed as a baby found it harder to deal with stressful events such as parental divorce.
The Swedish researchers believe close physical contact and mother-baby bonding during the first few days of life may be important factors.
Their work appears in Archives of Disease in Childhood.
The children's teachers were to rate the anxiety of their pupils on a scale of zero to 50, while parents were interviewed about major family disruption, including divorce or separation, which had occurred when their child was aged 5-10. The Karolinska Institute team also looked at other factors that might influence or be linked with a child's reactions to stress and coping mechanisms, including maternal depression, parental education levels, their social class, and smoking habits.
The children whose parents had divorced or separated were more likely to have high anxiety than their peers.
Specifically, breast-fed children were almost twice as likely to be highly anxious, while children who had been bottle fed were over nine times as likely to be highly anxious about parental divorce or separation.
The authors stress that their findings do not mean breastfeeding itself makes children cope better with life stress.
Rather, breastfeeding might affect the quality of the bonding between mother and child, and the way in which the two relate to each other.
The World Health Organization recommends that mothers should feed their babies on breast milk alone for the first six months of life.