A lawsuit filed in Minnesota, reported by ABC news, alleges that failures by Dr Michael Schulenberg played a "substantial part" in the star's death.
Prince died in 2016, aged 57, from an accidental overdose of the painkiller fentanyl, a powerful opioid.
Dr Schulenberg has denied any wrongdoing.
Earlier this year, prosecutors said no criminal charges would be brought over Prince's death.
But the family's lawsuit, filed in Hennepin County District Court on Friday, alleges that Dr Schulenberg's actions had played a part.