The suspect, Hayat Boumeddiene, arrived at an Istanbul airport on January 2 via Madrid and stayed in a hotel, Cavusoglu said in an interview with Anatolian.
Those dates would put her in Turkey before the violence in Paris began, and leaving for Syria while the attackers were still on the loose.
Seventeen people, including journalists and policemen, were killed in three days of violence that began with a shooting attack on the satirical newspaper Charlie Hebdo on Wednesday, January 7, and ended with a hostage-taking at a kosher supermarket on Friday. The three gunmen were also killed.
French police are searching for Boumeddiene, the 26-year-old partner of one of the attackers, describing her as "armed and dangerous".
Cavusoglu said as soon as Turkey identified the whereabouts of Boumeddiene, it passed the information to French authorities.
World leaders including Muslim and Jewish statesmen linked arms on Sunday to lead more than a million French citizens through Paris to pay tribute to victims of the attacks.