The group has attacked the Syl Hotel before, which is popular with government officials.
Witnesses reported blasts and gunfire coming from the hotel, telling agencies that fighters were still inside.
It was not immediately clear if there were casualties.
“The armed Mujahideen control the hotel and are shooting workers and officers” of the government in the hotel, al-Shabab said in a statement claiming responsibility for the attack.
Resident Farah Ali, who lives near the president’s office, told that: “We first heard a huge blast, and then gunfire followed. We understand the fighters are inside [the hotel] for we hear exchange of gunfire.”
“Several gunmen forced their way into the building after destroying the perimeter wall with a heavy explosion,” a security officer told to news agency.