Shareef said the seven men would be prosecuted over the attack.
He said that the police would not yet release their names because authorities were still searching for other suspects.
"I spoke to the assistant police commissioner and he said they are very, very close to cracking this case," Shareef said.
The injured included two Britons, eight Chinese nationals and two Japanese, all of whom suffered burn injuries, he said.
The British couple sustained burns of more than 40 per cent of their bodies.
The couple remain in hospital while the others have all been discharged and have left the country, Shareef said.
He said the bomb appeared to have been assembled by "a group of amateurs" and said investigators will seek help from Interpol, the US and India in investigating the blast.
Saturday's attack was the first-ever reported on the Indian Ocean archipelago and popular holiday destination.
Observers have expressed concern about the potential for violence in the overwhelmingly Muslim country due to political unrest.