According to the notice, Sukhu has brought "dishonour and discredit" to Dhumal through personal statements against him and his MP son Anurag Thakur over past four months.
Dhumal has asked him to tender an apology or face legal action.
The BJP leader, who sent the notice to Sukhu at his residence in native village in Hamirpur through his counsel, claimed Sukhu had tried to gain political mileage by maligning his image.
The notice mentions that if Sukhu does not apologise, the former chief minister would take action against him and will have the right to claim damages commensurate with his stature and reputation.
The notice refers to news items in some English and Hindi newspapers, quoting Sukhu having blamed Dhumal and his MP son Anurag Thakur for allegedly "commercialising politics in Himachal and selling the state to outsiders during the previous BJP regime".
State Congress President Sukhu, when contacted, said, "I have received the legal notice today only. I will go through it first and then comment."
