The fact that a country is entitled to require an International Certificate of Vaccination for yellow fever doesn't mean it will enforce such a requirement. As of the time of this writing, Brazil does not require proof of yellow fever vaccination for travelers coming from countries with risk of yellow fever transmission. Brazil recommends yellow fever vaccination solely for travelers who plan to enter areas in Brazil where the disease is endemic.
Sovereignty and Obligations
Brazil is a Member State of the World Health Organization (WHO) and bound to the International Health Regulations (2005), or IHR (2005), that entered into force in June 2007. The IHR (2005) are an international set of legally binding regulations which aim to prevent the spread of diseases on an international level.
World Health Organization Member States agreed upon the IHR (2005) by consensus. Compliance is grounded on a balance between sovereignty and shared commitment. The IHR (2005) don't include enforcement mechanisms because it is in each country's best interest to prevent dire consequences, such as high mortality and economic upheaval, that could stem from non-compliance.
Brazilian Ministry of Health Determinations
In November 2007, the Brazilian Epidemiological Surveillance Department and Health Surveillance Secretariat (Departamento de Vigilância Epidemiológica and Secretaria de Vigilância em Saúde), linked to the Brazilian Ministry of Health, issued a technical note determining that Brazil will only require the International Vaccination Certificate from travelers if the area they come from has become risky for the international spread of yellow fever.
According to the SVS, such a decision will be preceded by an evaluation of the case at hand and backed up by data from WHO and the Pan American Health Organization.
Item 8 of the same document states that should this situation arise, requirement of the International Certificate of Vaccination Certificate will be temporary, with yellow fever vaccination reverting to a recommended status as soon as the risk of international spread has been dismissed.
Other Countries' Requirements
Following the same principles mentioned above, other countries may require proof of yellow fever vaccination for a traveler who visited Brazil prior to entering their territory, since Brazil is one of the countries where the disease is endemic.
This World Health Organization document can be used as a reference about countries with risk of yellow fever transmission and countries that require yellow fever vaccination. However, if you plan on traveling to any of these countries after visiting Brazil, it is advisable to confirm at their consulate whether yellow fever vaccination requirements are being enforced at the time of your trip.

