Chief Justice Iftikhar Chaudhry issued the notice after reports in several newspapers quoted Pakistan People's Party leader Raja Riaz Ahmed as saying that Sharif holds dual nationality.
Chaudhry directed the Registrar's office to issue notices to Shareef and the editors of Assas, The News and Daily Times, and Ahmed, who is also the Leader of Opposition in the Punjab Assembly.
They were all directed to appear in person in the apex court on October 17.
Ahmed and the editors were directed to furnish "acceptable evidence" regarding the allegation that Sharif holds dual nationality.
The apex court is currently spearheading a drive against members of provincial and federal assemblies who have dual nationality.
It has ruled that persons holding foreign citizenship cannot serve as lawmakers.
The court has disqualified 11 lawmakers so far and said that Interior Minister Rehman Malik stands to lose his membership of the Senate or upper house of parliament as he had made a false declaration about his British citizenship at the time of the 2008 polls.