Katie Gee and Kirstie Trup, both 18 and from London, were on their way to dinner in Stone Town, an historic district of the island's capital, Zanzibar City.
Police say two man splashed acid on the women's faces and bodies as they drove by on a moped, and an investigation is underway to apprehend the men.
The young women, with consular assistance, are returning to their families Thursday night. The two women had been nearing the end of their three-week stint with the charity Art in Tanzania. Nicky Gee said her daughter's whole face and body has been burned by acid in the attack.
Authorities say a motive for the attack has not yet been established. Although Islam is the majority religion on the island, they say most islanders are happy to see tourists regardless of dress, and rarely antagonize their primary source of income.
Tanzania's minister of information, tourism, culture and sports, Said Ali Mbarouk, condemned the attack.
"We should co-operate with other government sectors to ensure that the perpetrators are arrested and brought to justice," he said.
"And I beg our nationals, this is not something they should be doing. Tourism is the strongest pillar of our economy, so if we do such acts we are killing our economy, and our livelihoods in general. So it is not an honourable thing to do, it's a bad thing and it should be condemned by all citizens of Zanzibar."
The British Foreign Office says that most of the 75,000 British nationals who visit Tanzania each year have "trouble free" visits, but that "violent and armed crime is increasing" and "there is an underlying threat from terrorism."
On the island of Zanzibar, it says, "incidents have taken place in Stone Town and on popular tourist beaches" including "mugging, bag snatching (especially from passing cars) and robbery," which have "increased throughout the country."
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