Senegal PM Mohammed Dionne said agreements with France would be respected but that Senegal would not extradite its citizens.
Interpol has issued a "Red Notice" for the arrest of Mr Diack, recently given a lifetime ban from the sport.
Mr Diack, son of ex-world athletics head Lamine Diack, has strongly denied the accusations against him.
He is accused by French prosecutors of being part of an alleged "system of corruption".
Mr Dionne told MPs said that, regarding the request from France, the instructions of President Macky Sall "are clear; we will not extradite our citizens".
Correspondents say Papa Massata Diack is believed to be in Senegal, where he gave an interview to a TV station last month, in which he said he would only answer questions from the French investigators if they travelled to Dakar.
The BBC's Abdourahmane Dia in Dakar says several political leaders and lawyers have already called on the Senegalese government not to extradite the former athletics marketing consultant, while some have suggested he could face trial in Senegal.
His father is in France and is not allowed the leave the country.
Lamine Diack is being investigated over allegations that he took payments for deferring sanctions against Russian drugs cheats while head of the IAAF.
Papa Massata Diack and Russian officials Valentin Balakhnichev and Alexei Melnikov were last month charged with multiple breaches of anti-doping rules relating to Russian athlete Liliya Shobukhova.
A report by the independent IAAF ethics commission panel said that they conspired to "blackmail" Shobukhova to cover up her doping violations by her paying them "bribes" of about Â£435,000 ($620,000).
Last month, Mr Diack told the BBC he "totally rejects" the blackmail allegations, saying: "There was no extortion of funds from any athlete."
The Interpol Red Notice says Massata Diack is wanted in France "on charges of complicity in receiving bribes, aggravated money-laundering, and conspiracy in an organised group to invest, conceal or convert the proceeds of active corruption".
Shobukhova's 38-month ban from track and field was reduced by seven months after she turned whistleblower for the World Anti-Doping Agency (Wada).
Senegal will not extradite Papa Massata Diack, accused of blackmailing athletes who failed drug tests, to France.