The deal allows Estonia to borrow up to 10 billion Swedish kronor ($1.1 billion) against Estonian kroons.
Estonia's central bank — Eesti Pank — called the move "a precautionary arrangement to secure financial stability and to promote confidence in the financial markets."
Sweden's Riksbank said it was important that the two countries help each other because their financial systems are closely linked. Swedish banks control more than 90 percent of Estonia's banking system.
"The Riksbank is therefore helping to reinforce Eesti Pank's ability to safeguard financial stability in Estonia," Riksbank governor Stefan Ingves said.
Estonia's economy contracted 9.4 percent in the fourth quarter from a year earlier, due to a steep decrease in manufacturing output and domestic demand. Estonia and neighboring Latvia are the worst performing economies in the European Union.
The central banks of Sweden and Denmark entered a swap agreement with Latvia in December.