They say that the bomb went off near the town of Anuradhapura.
A large military parade was earlier held under tight security in Sri Lanka's capital, Colombo, to mark the 60th anniversary of independence.
President Mahinda Rajapaksa told the parade the military were inflicting "unprecedented" defeats in their campaign against the Tamil Tigers.
Security forces had been placed on high alert after a weekend of violence.
At least 11 people were killed in a suicide attack at Colombo's main railway station on Sunday.
And on Saturday, 18 people died in another bus blast in the central town of Dambulla.
Both were blamed by the government on the Tamil Tigers rebels, though the rebels have denied involvement.
Attack fears
News of Monday's attack near Anuradhapura - which officials say killed at least five soldiers - came just after President Rajapaksa addressed a military parade in Colombo 60 years after it gained independence.
Health officials say that at least 16 people injured in the blast are being treated at Anuradhapura hospital.
The authorities have blamed Tamil Tiger rebels for that attack and another bomb blast in the south of the country which killed a soldier and injured five others.
The BBC's Roland Buerk in Colombo says that Monday's parade was a show of strength by Sri Lanka's armed forces - once again, officially at war with the Tamil Tigers.
"Our security forces are today achieving victories against terrorism unprecedented in history. Terrorism is receiving an unprecedented defeat," he said.
"In less than two years we have liberated the large Eastern Province that was under the clutches of the terrorists and confined them to two districts, only."
The president said that "the defeat of the most ruthless terrorists of the world in Sri Lanka is also a victory of the developed world".
"We are also fully committed to carry on this battle while safeguarding human rights. This is the reality," he said.
"In short, two years ago, no one believed that terrorists could be defeated. But, during the last two years we made it a reality in our motherland."
The Tigers have marked independence day by once again saying they will fight on for a separate state for the Tamil minority in the north and east.
"This is not a day of independence nor is it a day of celebration for our people," rebel spokesman B Nadesan said.
"The Sri Lankan government are still continuing its ethnic cleansing and mass killings among the Tamil people."
Sea fears
Ranks of soldiers, sailors and airmen were drawn up on grounds overlooking the Indian Ocean for Monday's parade.
Tanks and trucks carrying multi-barrelled rocket launchers rumbled past. Heavy guns fired a salute sending smoke drifting out over the blue water, our correspondent says.
Much of the centre of Colombo was been sealed off by military checkpoints.
Thousands of police and troops were deployed on the streets and the navy stepped up coastal patrols to combat a possible sea-borne attack.
Last month, the government pulled out of the 2002 ceasefire with the Tamil Tigers, arguing the rebels had used it to re-group and re-arm.
Since then, fighting has intensified on the frontlines that surround Tiger-held territory in the north.
Sri Lanka's army commander Lt-Gen Sarath Fonseka has said he now aims to defeat the rebels by the end of the year.
The Tamil Tigers have been fighting for an independent state in the north and east since 1983.
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