East of the capital Skopje, voting was halted in the town of Aracinovo after a gun battle.
Another shooting took place in the courtyard of a school serving as a polling station in the capital's Cair neighborhood.
"There were lots of shells from Kalashnikovs," said local resident Vanco Stojanoviski. "There were five or six [gunmen] with automatic weapons, Kalashnikovs, and one self-propelled grenade launcher."
The state news agency MIA reported scuffles in other areas and a small explosive device thrown at an empty cafe.
The incidents continue the violence that has marred much of the election campaign ahead of the vote -- including fighting between rival ethnic-Albanian parties and shootings and grenade attacks on party offices.
Outgoing Prime Minister Nikola Gruevski called the polls in April, hoping to secure an absolute majority for his center-right VMRO-DPMNE party.
The decision to return to the polls came after several events made it clear his ruling coalition could not continue.
One was deep divisions over whether to recognize the independence of northern neighbor Kosovo after the Albanian-majority region's declaration of independence from Serbia in February.
The Macedonian government did not recognize Kosovo as a state, and one of Gruevski's coalition partners withdrew in protest in March. Around a quarter of Macedonia's citizens are ethnic Albanians.
Then, adding to the political turmoil, came Greece's veto in early April of an invitation for Macedonia to join NATO.
Athens made the move because of a long-running dispute over the right to the name Macedonia, which is shared by a Greek province. Macedonia was admitted to the United Nations in 1991 as the Former Yugoslav Republic of Macedonia.
Today, the Kosovo and NATO issues are very much in Macedonians' minds as they flock to the polls to decide where their country goes from here.
Gruevski's party is the front-runner as it has sought to rally voters with appeals to national pride in the face of what it calls external pressures.
The party has promised not to change the name of the country under Greek pressure, to push on with reforms aimed at EU admission, to revive the economy, and to tackle corruption.
Speaking on May 30 at his party's closing rally in the eastern town of Strumica, Gruevski said Macedonians had "a right to be patriots."
"Don't be afraid of new decisions, do not run away from the responsibility, and don't be afraid of the feelings that bothered you for decades," Gruevski said. "You have a right to love your country, you have a right to be patriots, and you have rights to enter Europe with pride."
The appeals seem to have paid off, with recent opinion polls predicting a solid win for VMRO-DPMNE, with about 31 percent of the votes, ahead of the main opposition Social Democratic Union of Radmila Sekerinska and two ethnic-Albanian parties.
Polling stations were being watched by some 13,000 police and more than 6,200 monitors, including almost 500 from the international community.
The State Election Commission is expected to start providing preliminary results on the evening of June 1.