Almost one in 20 new fathers suffered depression in the weeks after their child was born, according to the study published in the journal JAMA Psychiatry.
At 18, girls whose fathers had experienced depression after their birth were themselves at greater risk of the condition, said Professor Paul Ramchandani from the University of Cambridge in the UK.
The "small but significant" increased risk applied only to daughters; sons were not affected, said Ramchandani.
One reason for this "handing on" effect could be that post-natal depression in fathers is sometimes linked with an increased level of maternal depression, researchers said.
This might mean that family life is more disrupted for everyone with higher levels of stress for all, researchers said.
It may also be that the having one or both parents with depression affects the way in which parents interact with their children, they said.
It is unclear why girls may be more affected at this age, according to the study.
There may be links to specific aspects of father-daughter relationships as girls go through adolescence, the researchers suggest.
The findings are important because they have implications for perinatal services, which have traditionally considered post-natal depression to be a potential problem for mothers only.
They highlight the importance of recognising and treating depression in fathers during the postnatal period, and call on health professionals to consider both parents when one reports depression.
"Research from this study of families in Bristol has already shown that fathers can experience depression in the postnatal period as well as mothers," Ramchandani said.
"What is new in this paper is that we were able to follow up the young people from birth through to the age of 18, when they were interviewed about their own experience of depression," Ramchandani said.
Those young people whose fathers had been depressed back when they were born had an increased risk of depression at age 18 years, researchers said.
It appears that depression in fathers is linked with an increased level of stress in the whole family, and that this might be one way in which offspring may be affected, they said.
The findings highlight the importance of providing appropriate help to fathers, as well as mothers, who may experience depression.