The ministry said in a statement that exchanges of gunfire have been reported over the last two days at numerous points along Azerbaijan's western border. Armenia had said earlier that three of its soldiers died in the clashes.
Azerbaijan and Armenia have for two decades been at odds over the disputed Nagorno-Karabakh territory, which lies within Azerbaijan, but was taken over by Armenia during a six-year war that killed about 30,000 people and displaced 1 million.
The incidents come just as U.S. Secretary of State Hillary Rodham Clinton has embarked on a tour of the South Caucasus in the hope of mediating progress in territorial disputes in the region.
Azerbaijan's defense ministry said one clash took place near the village of Ashagy Askipara early Tuesday morning, after their soldiers were attacked by Armenian commandos. Four Azeri troops were killed in the fighting, officials said. Another soldier died in a separate incident, the ministry said.
Armenia on Monday said three of its soldiers were killed and another six were wounded in villages nearby.
Clinton decried the "senseless deaths of young soldiers and innocent civilians" as part of the Nagorno-Karabakh conflict - just hours after Monday's border clash.
"I am very concerned about the danger of escalation of tensions and the senseless deaths of young soldiers and innocent civilians," Clinton told reporters after a dinner with Armenia's president and foreign minister. "The use of force will not resolve the Nagorno-Karabakh conflict," she said, urging the sides to refrain from violence.
Warning that Azeri-Armenian tensions could escalate into a broader conflict with terrible consequences, Clinton said the US would continue to press with France, Russia and others on mediation efforts.