A senior security source said some of the hostages had been freed after being made to recite verses from the Koran. The French newspaper Le Monde quoted the Malian security ministry as saying at least three hostages had been killed.
The raid on the Radisson Blu hotel, which lies just west of the city center near government ministries and diplomatic offices in the former French colony, comes a week after Islamic State militants killed 129 people in Paris.
The identity of the Bamako gunmen, or the group to which they belong, is not known.
Northern Mali was occupied by Islamist fighters, some with links to al Qaeda, for most of 2012. They were driven out by a French-led military operation, but sporadic violence has continued in Mali's central belt on the southern reaches of the Sahara, and in Bamako.
The security source said as many as 10 gunmen had stormed the building, firing shots and shouting "Allahu Akbar", or "God is great" in Arabic. The hotel's head of security said two private security guards had been injured in the early stages of the attack, which began at 7 a.m. (0200 ET).
A French presidential source said French citizens were in the hotel. The Chinese state news agency Xinhua said several Chinese tourists were among those trapped inside the building. Turkish Airlines also said it had six staff inside.