Hopper died of complications from prostate cancer in in 2010. He was 74.
TMZ said Tuesday court documents show the "Easy Rider" and "Apocalypse Now" actor provided for his youngest child Galen by instructing his executors to set up a trust for her.
Hopper was in the middle of divorcing his wife Victoria Duffy, the child's mother, at the time of his death.
Duffy attempted to claim part of the late actor's estate, but was unsuccessful due to a pre-nuptial agreement.
TMZ said Duffy will have no control over the money in her daughter's trust.
Hopper also had three adult children from previous relationships. The celebrity news website did not say what, if anything, they inherited after their father's death.