Three people including a French citizen have been confirmed to have died in the siege.
Malian security sources said jihadists had launched a shooting rampage in the 190-room hotel and automatic weapons fire could be heard from outside the building.
Islamist groups have continued to wage attacks in Mali despite a June peace deal between former Tuareg rebels in the north of the country and rival pro-government armed groups.
Malian security has taken control of the security situation and efforts to rescue the held hostages are ongoing.
Radisson Blu hotel is popular with visiting Western officials and is a frequent base for Air France staff.
This could be planned aftermath attack after the attack in Paris that led to the death of 129 people.