"They [the protesters] tried to pass through the police cordon and make their way onto the territory where the exercises are being held. They threw stones at military, who had to open fire into the air," Alexander Dombrovsky said, adding that no one was hurt or detained.
Protesters said the police had beaten women who participated in the protests.
The Ukrainian Defense Ministry said the Crimea protests had not affected the exercises.
The Bratstvo (Brotherhood) Ukrainian opposition party press service said on Monday that the party had prevented foreign warships participating in the naval exercises from leaving the Black Sea port of Odessa.
Sea Breeze 2008 began last Monday in Ukraine's Odessa, Crimea and Black Sea coastal regions. Two years ago, the Sea Breeze 2006 exercise in the Crimea was also disrupted by protests.
Ukraine and the United States are joined by 15 other countries for this year's exercises, which are due to end on July 26. Fifteen Ukrainian ships, four aircraft, 10 helicopters, and 500 service personnel are involved in the military exercises.
The Ukrainian Progressive Socialist Party said on Wednesday that authorities in the Odessa region had banned broadcasts by Russian television channels over their coverage of the exercise and accompanying protests.
Ukraine's pro-Western leadership has been pursuing NATO membership since President Viktor Yushchenko came to power in 2004. Ukraine failed to secure a NATO Membership Action Plan, a key step toward joining the alliance, at a NATO summit in April, but was told the decision would be reviewed in December.
A poll conducted in April by the FOM-Ukraina pollster indicated that a majority of Ukrainians oppose NATO membership.