"We recommend avoiding travel to Russia altogether. Estonian citizens temporarily staying in Russia are advised to consider the necessity of staying in Russia and return to Estonia if possible," says the Ministry's travel information advice website.
"Due to migratory pressure, Estonia may temporarily close its border crossing points at short notice and it will no longer be possible to return to Estonia via the crossing points," it says.
According to earlier travel information, the ministry advised against traveling to Russia "without an urgent need", referring to Russia's military activities in Ukraine.
Minister of Foreign Affairs Margus Tsahkna (Eesti 200) said at the government's weekly press conference on Thursday that he had discussed the issue in Brussels this week. Estonia is ready to close the border if necessary.
"Therefore, this is also an important message to all our citizens that if Estonia temporarily closes its borders, those who are in Russia will not be able to return. And that is why there is a very clear advice not to travel to Russia. Because we don't know when the migratory pressure on our borders might rise to the point where we have to close our borders temporarily. But this preparedness is in place and is being led by the Ministry of Interior," the minister said.
The MFA recommends that Estonian citizens temporarily staying in Russia register their stay on its website.
It also said people with dual citizenship can end up being sent to fight on Russia's behalf in Ukraine: "Estonian-Russian dual nationals are treated as Russian citizens by the Russian Federation, and Estonia's ability to provide consular assistance, including on mobilization issues, is limited."
The ministry also said Russian border guards may check the content of personal electronic devices, including social media, when people cross the border.
After Estonia's consulates were closed in St Petersburg and Pskov, the only place consular assistance can be sought is in Moscow.
The MFA did not want to comment on rumors about Russia introducing a "loyalty agreement" for border crossers. A spokesperson said this is a plan, not a step that has already taken place.
The ministry's website highlights Russia has the right to change its entry rules as it sees fit and other countries may not be notified immediately.
More than 700 migrants, mostly from the Middle East and Africa, have been directed to Finland's borders over the last month. Authorities, and the migrants, say Russia is organizing this activity.
Estonian ministers have called it a hybrid attack that follows similar situations on the Latvian, Lithuanian, and Polish borders with Belarus.
The authorities are now observing the situation to see if the migration redirects to Estonia's borders. Barriers have already been placed at the Narva border.
Editor: Mait Ots, Helen Wright