Foreign Office said it was urgently checking reports that a Briton was among those killed – the majority were reported to have been French and Moroccan.
William Hague, the Foreign Secretary, said he was "shocked and saddened" by the attack.
“British officials are in contact with the Moroccan authorities to establish the facts and to provide consular support to any British nationals who may have been caught up in the blast."
The explosion went off just before midday and tore the facade off the two-storey Argana café in Jema el Fna square, a UNESCO World Heritage site at the heart of Marrakesh's old town.
Witnesses at the scene described seeing a man enter the café and order an orange juice before "blowing himself up". Another said the bomber entered the café, dropped a suitcase and walked straight out.