President Vladimir Putin's order of a "partial" military mobilisation has prompted some Russians to protest on the streets.
Others have fled, fearing they could be called up to serve in Ukraine.
One-way flights to nearby countries have now sold out, while Google recorded a spike of people searching for ways to leave Russia.
Since Monday, Russian citizens can only enter the European Union via the 1,340-kilometre border with Finland. Unlike the Baltic nations and Poland, Finland has not completely restricted the entry of Russian tourists with Schengen visas.
Putin's speech prompted misleading rumours that some Russians had joined lengthy queues at Finland’s southeastern border on Wednesday night, hoping to leave the country. Euronews has fact-checked the claims.
A number of images and videos were shared online, showing long lines of stationary traffic at Finland's border.
Some users falsely claimed that the queues and traffic jams were as long as 35 kilometres and were “rising by the hour”.
One such video of the Vaalimaa border post in southeastern Finland gathered more than 2.8 million views on Twitter.
However, an online investigation reveals the footage was first shared online on 19 September, two days before Putin's mobilisation call.
The owner of the video, who posted the clip on both YouTube and TikTok, also states that it was filmed “two weeks earlier” at the end of August and that the congestion was "normal" for autumn border crossings.
His claims have also been supported by the Finnish Border Guard Service.
"There is normal queuing in border traffic," said Matti Pitkäniitty, the head of the International Affairs Unit at the Finnish Border Guard.
"The situation at [the] Finnish-Russian land border remains normal," he wrote on Twitter.
The regional border service added that queues on Wednesday at the border inspection were only "250 metres" long, and certainly not 35 kilometres.
On Thursday, queues at the Vaalimaa border post were approximately 500 metres long, they added.
"[The] situation at Finland's borders has not changed with the announcement of Russian mobilisation," the Border Guard service added on Twitter.
"There are videos circulating on social media, at least some of which have already been filmed before and now taken out of context. There is incorrect information in circulation."
Pitkäniitty later confirmed that 4,824 Russians arrived in Finland via the eastern border on Wednesday.
While this was an increase on the previous week -- 3,133 Russians arrived on September 14 -- the number was "lower than a normal weekend". On Thursday, 6,470 Russians arrived in Finland across the land border, while 3,227 travelled in the other direction.
"In August and September, we have had around 6 000 arriving in Finland on Saturdays," Pitkäniittywrote on Twitter. "We are at the level of weekend traffic."
The false rumours of kilometre-long queues were also debunked online by Ville Cantell, a director at Finland's Ministry for Foreign Affairs.
The Border Guard Service did confirm on Thursday that border traffic from Russia was "busy" and "brisk", but stressed that the situation was "under control".
"Incoming traffic at the eastern border increased during the night," the authority wrote on Twitter.
"Traffic has increased compared to previous weeks, but the amount is still small compared to the time before the pandemic. Our resources are sufficient and the situation is under the control."
Southeastern Finland's border guard has recently reported an exceptional number of "high quality" false and forged travel documents in cross-border traffic.
"The people who submitted the forgeries were from the Caucasus region and their destinations were mainly in Central Europe," the authority said in a statement on Tuesday
Some people have paid several thousand euros for the forged documents to try and illegally enter Finland, they added. An investigation is underway.
Finland’s decision to allow some travellers to cross the EU's longest border with Russia had faced criticism, including from Ukraine's foreign minister Dmytro Kuleba.
"Time to stop accepting tourist visas from Russia," Finnish MEP Miapetra Kumpula-Natri wrote on Twitter.
"Russian visa applications need to have reasons for entering and processed accordingly. [The] border cannot remain open normally."
Finland's foreign minister Pekka Haavisto has indicated that the country is urgently preparing measures to restrict Russian tourist visas.
"Finland does not want to be a transit country for Schengen visas issued by other countries," he told national media.
"There is no moral justification for Russian holidays to continue as they are."