Kirstie Trup and Katie Gee, both 18, were doing volunteer work in the country when they were injured when acid was thrown in their faces. Last week a Catholic priest was attacked in the fifth acid attack in Zanzibar since November.
Police commissioner Mussa Ali Mussa said some of those arrested have links to al Qaeda and Somali Islamic extremist group al-Shabab.
Earlier police have seized 29 litres of acid from different people, saying they were illegally in possession of it.
Some questioned the police claim that terror groups may be involved and have a presence in Zanzibar.
Zanzibar is unlikely to have an al-Shabab or al Qaeda presence, said Ahmeid Rajab, the managing director of the Somali satellite television network, Universal TV.
Police are looking for another excuse to escape blame for failing to arrest real suspects and instead they are going after innocent people, said Mr Rajab.