In a joint statement, the banks said their "precautionary arrangement to secure financial stability and to promote confidence on the financial markets" would allow the Estonians to borrow up to 10 billion kronor ($ 1.12 billion).
"The agreement increases the capability of Estonia's central bank to secure financial stability," its chief Andres Lipstok told reporters.
"The agreement is a sign of the importance of cross-border cooperation in the current world where financial markets are so integrated," he said.
Central bank spokeswoman Livia Kulm cautioned that the deal "is in no way a sign that things have got worse in Estonian banking."
Estonian authorities have repeatedly insisted that they will not have to follow the lead of neighbouring recession-casualty Latvia, where the government in November took over the nation's second-biggest bank, Parex, after a depositors fled.
Sweden is heavily exposed to the economic crisis in Estonia and fellow Baltic states Latvia and Lithuania because its banks dominate their markets and its companies are among the region's top investors.
"It is important that central banks cooperate and assist each other in times of financial stress. The financial systems in Estonia and Sweden are closely linked," the governor of Sweden's central bank, Stefan Ingves, said in a statement.
A Soviet-ruled state which regained independence from Moscow in 1991, Estonia long enjoyed a reputation as a "Tiger" in the European Union, which it joined in 2004, with growth rates of 10.4 percent in 2006 and 6.3 percent in 2007.
But it tipped into recession last year in the face of double-digit inflation and tighter credit rules, as well as the global crisis which hit exports of goods and services.
Output shrank 3.6 percent in 2008 and is expected to fall by up to 8.9 percent this year.