The controversial law, which was narrowly voted through Sweden's parliament last month and is set to take effect next year, will enable the National Defence Radio Establishment (FRA) -- a civilian agency despite its name -- to tap all cross-border Internet and telephone communication.
Sweden is one of several large Internet hubs in Europe, transmitting Internet traffic from other countries through its cables.
Finnish-Swedish telecoms operator TeliaSonera told AFP this week it had decided last year to move its servers from Sweden to Finland when the Swedish government announced plans for its new monitoring law.
"Many of Sonera's Finnish customers and Finnish authorities expressed their concerns about communications within Finland being monitored by a third party," TeliaSonera Finland's spokesman Ahti Martikainen said.
"That is why we moved servers serving our Finnish customers to Finland in April," he said.
In Denmark, a citizens' rights group, TI-Politisk Forening, has meanwhile demanded "an end to the Swedes' surveillance of the world's Internet traffic."
At least one left-wing opposition party has urged Danish Prime Minister Anders Fogh Rasmussen to raise the issue with the Swedish government, a call he has so far rejected.
In Norway, the government on Thursday ordered the national telecom agency to study the impact the Swedish law will have on Norwegian interests.
"Right now we are collecting the information. This has high priority," Elisabeth Sørbøe Aarsæther, press chief at the country's Post and Telecommunications Authority told AFP on Friday.
The law has sparked a wave of opposition in Sweden, where critics fear the creation of a "big brother" state.
The defence ministry has insisted the legislation is necessary as communications are increasingly transmitted through fibre-optic cables.
Several intelligence experts interviewed in Swedish media in recent days have argued the criticism is unwarranted, claiming that other countries carry out similar monitoring but don't make it public knowledge.
The Svenska Dagbladet daily reported on Wednesday that unnamed sources closely
connected to Swedish intelligence believed the law was mainly aimed at eavesdropping on Russian data traffic that passes through the country.