Poland, Estonia, Latvia and Lithuania all closed their borders to Russian tourists earlier this month.
But Russians will still be allowed to visit family or for work and study in Finland, the foreign minister said.
The decision comes after the number of Russians arriving at the border surged following a call-up of 300,000 military reservists by President Vladimir Putin.
Queues have formed at border crossings as people try to flee, including long lines at Russia’s border into Georgia, which does not require a visa for travel.
Finland – which shares a 1,300km (800 mile) border with Russia and does require a visa – also reported an increase in people trying to cross the border following the partial mobilisation.
Speaking on Thursday, Finnish Foreign Minister Pekka Haavisto told a press conference the mobilisation order had a “significant impact” on its decision.
“The decision aims to completely prevent the current situation of Russian tourism to Finland and the related transit through Finland,” he said.
The move comes into force at midnight and also bans Russians with Schengen tourist visas from entering the country.
Mr Haavisto also said the flow of Russians was seen as endangering Finland’s international relations.
Russians visiting Finland will now need to apply for a visa in advance at a centre in Russia, with an invitation either from a business or personal contact.
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