Brigadier Udaya Nanayakkara, a military spokesman, said: "There has been an explosion in Ampara town a little while ago. Eleven civilians were killed and 29 injured. It is definitely by the LTTE."
The LTTE did not immediately comment on the incident.
Police said the target of blast in the crowded New City Cafe was unclear, despite a government minister's convoy passing through the area minutes beforehand.
The injured were taken to the local Ampara hospital. Police said nine women and two men died in the attack.
Fighting has intensified between the Tamil fighters and government forces along the northern frontier between the two groups in recent months.
Security along the eastern coast has been stepped up for the elections in Batticaloa, Trincomalee and Ampara on Saturday to elect officials to run the eastern provincial council.
The military had expelled Tamil fighters from large areas of the east, formerly a LTTE stronghold, in July 2007.
'Hearts and minds'
The elections are part of Mahinda Rajapakse's, Sri Lanka's president, government's policy to devolve power to minority Tamil areas, which they hope will occur in parallel with a military victory over the LTTE.
Rajapakse has expressed his desire to win the "hearts and minds" of "liberated" Tamils affected by the war by devolving power.
It is a policy the government also wants to take to northern areas held by the LTTE.
Tens of thousands of people have died in the war in which the LTTE are attempting to gain a separate homeland for minority Tamils in the island's north and east.