The carnage in Burkina Faso's capital marks a new expansion for al-Qaeda's North African branch.
Burkina Faso's government says 28 people were killed and a further 56 injured.
This is the first time that AQIM has claimed credit for a high-profile attack in the country.
But it has been active in several countries in the region, including Mauritania, Mali, Niger and its home, Algeria.
While al-Murabitoun has previously carried out several attacks in Mali, the group was not known to be behind any significant activity in neighbouring Burkina Faso.
The group had previously said that it was behind the abduction in April of a Romanian national in the north of Burkina Faso and issued a video featuring a plea for help by the hostage who worked for a mining company.
The attack on the Splendid Hotel in Burkina Faso is reminiscent of a similar armed assault that targeted the Radisson Blu hotel in Mali's capital, Bamako, in November last year.
That involved mass shootings and hostage-taking. Both hotels were reportedly frequented by UN staff as well as Western nationals.
The latest attack also bears striking similarities to the January 2013 attack on the In Amenas gas facility in southern Algeria by al-Murabitoun, which is led by the Algerian veteran jihadist Mokhtar Belmokhtar. At least 39 foreign hostages were killed.
The Bamako hotel attack was claimed jointly by AQIM and al-Murabitoun. The claim of responsibility was soon followed by a merger between the two groups.
AQIM's leader, Abu-Mus'ab Abd-al-Wadud (aka Abdelmalek Droukdel), warned the French people of further attacks against them if they failed to prevent their government from "leaving alone" Muslims and their lands.
AQIM issued a short written statement via its official account on Twitter on the day of the attack in Burkina Faso in which it indicated that Westerners and UN staff were the target.