The protesters, many carrying banners from half a dozen Islamist groups, burnt an effigy of Barack Obama outside the national Baitul Mokarram Mosque, the country's largest, after Friday prayers.
They also set fire to a French flag as they carried placards and banners reading "Obama, you are a cheater", "Protest the disgrace of Prophet Muhammed!"
Security was tightened around the protest area with the deployment of hundreds of police and elite Rapid Action Battalion, armoured personnel carriers and water cannon.
French authorities in Bangladesh also shut down three cultural centres and the French embassy in the capital, police said.
About 90% of Bangladesh's 153 million people are Muslims.
The government has condemned the film and blocked the video-sharing website YouTube, where the film was uploaded.