Ukraine's Channel 5 television quoted Vladislav Seleznyov as saying the shooting, a rare occurrence since Russian forces took over the Black Sea peninsula a week ago, took place in mid-afternoon at a motor pool base near Bakhchisaray.
On his Facebook page, Seleznyov said about 10 "unidentified armed men" in two minibuses drove into the compound and demanded Ukrainian personnel there give them 10 trucks.
Earlier, Interfax Ukraine news agency quoted an unnamed Ukrainian official describing the men as Russian troops and saying that none of the Ukrainians at the site was injured in the shooting.
Moscow, which has a major naval base at Sevastopol in Crimea, has denied that uniformed units, wearing no insignia, which have taken control of the region are from its military forces - a denial ridiculed in Kiev and by Western governments.
Crimean leaders who took power after Ukraine's pro-Moscow president was overthrown in Kiev have called a referendum for Sunday to unite the region with Russia.Officials could not immediately be contacted and it was unclear whether the confrontation at Bakhchisaray had ended.