The deaths on Monday, near the town of Panama, in the district of Ampara, come just days after the government and the Tigers agreed to hold talks on ending the violence that has killed hundreds of people since late July.
The victims were taken to the Jumma Mosque as shops were closed in protest against the killings which each side has blamed on the other.
A military spokesman said the workers had gone to renovate a sluice gate and went missing.
"They have been found dead, hacked and chopped," he said. "Some of the bodies have been chopped into pieces."
The defence ministry initially reported that 11 people had been killed but later confirmed that one man survived but was badly injured.
"This act by the Tiger terrorists indicate that not only are they out to obstruct and sabotage the reconstruction ... but are also prepared even to massacre those [who] are engaged in any humanitarian work," the ministry said.
"The LTTE [Liberation Tigers of Tamil Eelam] condemns the massacre of 11 Muslim workers," the Tamil Tigers said in a statement denying involvement in the killings.
They said the massacre took place in a Sri Lankan government controlled area where there is a military camp. "The Sri Lankan military is adopting its long tradition of blaming the LTTE for the atrocities it commits," the separatists said.
Nordic truce monitors are going to visit the scene.
Muslims are the second-largest minority after ethnic Tamils, who are mostly Hindu, and generally oppose the Tamil Tigers, who have accused them of supporting the government.
The separatists also oppose Muslims cultivating land in areas they consider to be Tamil territory.
Separately, a Sri Lankan soldier was killed and another wounded in an overnight attack by suspected separatists in the country's troubled north, the military said.
The Tamil Tigers are fighting for a
separate homeland in the north
Norway announced last week that the government and the Tigers had agreed to meet for talks for the first time since they pulled out of negotiations in April.
But both sides have imposed conditions before the talks that few expect either to honour.
The Tigers want the army to end offensive operations and give back captured territory in the northeastern harbour of Trincomalee.
The government has demanded a written guarantee from the Tigers that they will stop attacks, and have also urged them to lay down arms.
The separatists have been fighting since 1983 for a separate homeland for the country's 3.2 million ethnic Tamil minority in the northeast, complaining of discrimination by the mostly Buddhist Sinhalese majority, which make up nearly three quarters of the 20 million population.
The conflict had cost the lives of about 65,000 people before a cease-fire in 2002, but hundreds have been killed and more than 220,000 - mainly Tamils and Muslims - driven from their homes since December.