A poster of Macron was set alight in the port city of Chittagong, where authorities said another 4,000 people took part in protests.
Smaller rallies were held in other towns across the Muslim-majority nation of more than 160 million people.
Turkish President Recep Tayyip Erdoğan's office vowed to take "legal and diplomatic action" over the cartoon, while the country's NTV broadcaster said Ankara had summoned a senior diplomat from the French embassy.
Iran's supreme leader Ayatollah Ali Khamenei called Macron's defence of the publications a "stupid act" and an "insult" to those who voted for him.
Pakistan's Prime Minister Imran Khan on Wednesday wrote to leaders of Muslim countries calling on them to act together against Islamophobia.