Jeune Afrique's suspension marks the latest escalation in a crackdown on French media since the West African country fell under military rule last year.
The statement accused the publication of seeking to discredit the armed forces and of manipulating information to "spread chaos" in the country following two articles published over the past four days.
Jeune Afrique did not immediately respond to an emailed request for comment.
Relations between Burkina Faso and its former coloniser France have soured since frustrations over worsening insecurity linked to a jihadist insurgency spurred two military takeovers last year.
These tensions have led to expulsion orders for diplomatic officials, including the French ambassador to the country, and fuelled a backlash against foreign media.
The junta has already suspended French-funded broadcasters Radio France Internationale and France24 for allegedly giving voice to Islamist militants staging an insurgency across the Sahel region south of the Sahara. Both publications denied the accusations.
French television channel La Chaine Info, of private broadcaster TF1, was suspended for three months in June for airing a report on the insurgency that "lacked objectivity". TF1 declined to comment at the time.
In April, two French journalists working for newspapers Le Monde and Liberation were expelled from the country.
Liberation said the suspension was unjustified as the two journalists were of "perfect integrity" and had all their paperwork in order.
