Sergei Ivanov made the comments during a speech in Sevastopol, the home of Russia's Black Sea Fleet, to mark the 225th anniversary of the Ukrainian city.
"A second consequence of NATO membership for Ukraine will be introducing a visa regime, as NATO will insist Ukraine introduce one," Ivanov told journalists.
"I seriously doubt that the number of Russian tourists as a result [of the introduction of visas] will increase and their place taken by American, English and German tourists," he added.
The country's pro-Western leadership has been pursuing NATO membership since 2004, when President Viktor Yushchenko came to power. Ukraine failed to secure membership in the 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.
Russia staunchly opposes the post-Soviet country's NATO ambitions, and the Kremlin threatened in February to retarget missiles at Ukraine if it joins NATO.
Sevastopol on the Crimean peninsula is the focus of an ongoing dispute between Moscow and Kiev. Ukraine wants to set a deadline for Russia's lease of naval facilities in the Crimea, while some senior Russian officials have questioned Ukraine's right to sovereignty over Sevastopol.
Frequent disputes have arisen between Russia and Ukraine over the lease of the Sevastopol base. Moscow Mayor Yury Lyzhkov was barred from entering the Ukraine in May for publicly saying the area is rightfully Russian territory.
According to the Moscow mayor, Soviet leader Nikita Khrushchev gave the Crimea to Ukraine in 1954 as "a token of brotherly love," but under a 1948 decree Sevastopol was assigned special city status "under the governing central authorities," and, therefore should not have been included in the list of territories transferred to Ukraine.
The Crimea, now an autonomous region within Ukraine, is a predominantly Russian-speaking territory. Since the 1991 breakup of the Soviet Union, the Crimea has unsuccessfully sought independence from Ukraine. A 1994 referendum in the Crimea supported demands for a broader autonomy and closer links with Russia.
