The disappearance has been reported to the police in Sweden and has been classified as a kidnapping, according to a report in the Expressen daily.
The Foreign Ministry has also been briefed about the case.
"When It comes to missing persons, it's a police matter," said Anna Ekberg at the ministry press office.
"We are trying to gather as much information as we can on the matter," she added.
Police in Tanzania say that they have been in contact with Swedish police via Interpol, but are referring all questions about the missing three to Swedish authorities.
However, the Swedish police have so far been unwilling to comment on the case.
"We never comment on any kidnappings of Swedes abroad," said Fredrik Wallén at the national police press office.
There is currently no further information about where in Sweden the trio originate from nor what they were doing in the east African country.