Combating International Islamophobia Act This bill establishes within the Department of State the Office to Monitor and Combat Islamophobia and addresses related issues. The office shall monitor and combat acts of Islamophobia and Islamophobic incitement in foreign countries. The bill establishes the position of Special Envoy for Monitoring and Combating Islamophobia, who shall head the office. The bill also requires certain existing annual reports to Congress about human rights and religious freedom in foreign countries to include information about Islamophobia, such as information about (1) acts of physical violence or harassment of Muslim people, (2) instances of propaganda in government and nongovernment media that attempt to justify or promote hatred or incite violence against Muslim people, and (3) actions taken by a country's government to respond to such acts. The office shall coordinate and assist in preparing these portions of the reports. No funds made available pursuant to the bill may be used to promote or endorse a boycott, divestment, and sanctions movement ideology (i.e., economic measures against Israel or Israel-related individuals or organizations) or used to promote or endorse a Muslim ban.