Governor Vasily Golubev says the measure was enacted after the region saw an increase in refugees due to evacuation orders by pro-Russian separatist leaders.
A Russian region bordering Ukraine has declared a state of emergency, citing growing numbers of people arriving from separatist-held areas in Ukraine after they received evacuation orders.
"Given the trend of increasing numbers of people arriving, we consider it appropriate to introduce a state of emergency," the Rostov region's governor Vasily Golubev said in a meeting on Saturday, according to Russian news agencies.
The current head of Russia's emergencies ministry said some 400 people as well as 150 vehicles were involved in operations to receive people arriving from separatist territory.
State-run news agency RIA Novosti reported that those crossing checkpoints were being offered medical and psychological support.
Emergency services in the Donetsk separatist region has said earlier Saturday that just over 6,600 people have been evacuated.
The Lugansk region meanwhile said 25,000 people had left of their own accord and convoys were readying to take out an additional 10,000 people.
Earlier, the leaders of two pro-Russian separatist republics in eastern Ukraine on Friday had ordered civilians to cross the border into Russia, accusing the Ukrainian army of preparing to try and retake the regions by force.
Russian President Vladimir Putin ordered his government on Friday to give evacuees about 100 euros (10,000 rubles).
Kiev has repeatedly denied any plans to regain control of separatist-held areas by force.
The conflict in eastern Ukraine erupted in 2014 when Moscow-backed rebels broke away from Kiev and Russia annexed the Crimean peninsula.
Some 14,000 people have been killed in fighting since then.