Up to 20 people are reported to have been killed and 15 wounded in explosions and gunfire around the hotel in Ouagadougou, which witnesses reported was partly on fire.
Around 10 vehicles were on fire in the streets near the 146-room Splendid Hotel.
The Burkina Faso government said on Twitter that 33 people had been freed after commandos stormed the hotel, including minister Clement Sawadogo.
Both the hotel and the cafe are popular with United Nations staff and foreigners. It is located in a busy central area of the capital, not far from the airport.
"First, they set fire to the vehicles to the surroundings before entering the hotel. "They are wearing turbans and in masks. They all had beards. "They said they were acting on behalf of the Islamic State."Mr Diallo also said there were between 100 to 150 people in the hotel at the time of the attack as many guests were having dinner.
Another eyewitness, named only as Mathieu, said:
"I was en route to the Akino Faso hotel, arriving at Kwame Nkrumah I saw some cars coming front the other direction which shot at the hotel.
"When I continued towards the hotel there was a (V8) which blocked the way but there was a small space to pas through so I went through it.
"At the same tome I saw three men in turbans with Kalashnikovs who came out of the hotel and started to shoot at the air about 10metres from me.
"I fled from the situation, but I had the time to see two bodies on the floor outside Cappuccino cafe, they were white people.
"At the same moment, there was an explosion in the hotel. "It was not a shot, it was an explosion. "
"So I circumvented the hotel and tried to look for my mother and ask her if we could go back to hers.
"When I passed Kwame Nkurumah again to leave, a man in front of me took a bullet through his passenger door.
"He opened the door and fell out of his car. A firefighter who passed by had seen him and got out to help him. "While I looked for a way to escape there was a disturbance in the street and people started shooting to clear people way. "When I left there was still no order in the place."
"Terrorist attack on Avenue N'Krumah. Avoid the perimeter."Flight radar tracking sites also suggested an Air France flight had to divert its path away from Ouagadougou.
Burkina Faso has remained politically unstable since October 2014 when veteran President Blaise Compaore was overthrown in a popular protest.