A senior security source and the hotel’s operator said the attack occurred early on Friday morning.
No casualty figure has been given.
The raid on the Radisson Blu hotel, which lies just west of the city centre near government ministries and diplomatic offices in the former French colony, comes a week after Islamic State (IS) militants killed 129 people in Paris.
The identity of the Bamako gunmen, or the group to which they belong, is not known.
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.
Witnesses in the area said police had surrounded the hotel and were blocking roads leading into the neighbourhood.
The Chinese state news agency Xinhua said several Chinese tourists were among those trapped inside the building.
The company that runs the hotel popular to foreigners in Mali, Rezidor Group, said it understood that there were two gunmen.
“According to our information, two people are holding 140 clients and 30 employees,” it said in a statement quoted by the BBC.
A senior member of the hotel’s security detail said two private security guards had been injured in the early stages of the attack, which began at 7 a.m. (0700 GMT).
The U.S. Embassy tweeted that it was “aware of an ongoing active shooter operation at the Radisson Hotel,” and instructed its citizens to stay indoors.
An Islamist group claimed responsibility for the death of five people last March in an attack on a restaurant in Bamako that is popular with foreigners.
Northern Mali was occupied by Islamist fighters, some with links to al Qaeda, for most of 2012. Although they were driven out by a French-led military operation, sporadic violence has continued.