The restrictions included a requirement that the Black Sea fleet seek the permission of Ukraine's armed forces "at least 72 hours prior to ships or aircraft crossing the Ukrainian border," Yushchenko's office said in a statement.
If Russia does not fulfill the new requirements, Ukraine "may demand that naval ships...and aircraft of the Black Sea fleet leave" Ukraine's territory immediately, the statement said.
The announcement ratcheted up tensions between Russia and Ukraine, which has given political support to Tbilisi during Moscow's military conflict with Georgia.
Yushchenko has pursued a staunchly pro-Western course, like Georgia seeking membership of the North Atlantic Treaty Organization, whose expansion Moscow strongly opposes.
Ships from the Black Sea fleet have been active off the coast of Georgia.
Russia's military Sunday said it had sunk one Georgian naval vessel.
Tuesday, Georgia said Russia had sunk three Georgian coastguard ships.
Russia has maintained its historic Black Sea fleet base in Sevastopol since the 1991 Soviet collapse and the current Russian lease on the facility expires in 2017.
Russian politicians and military officials are strongly opposed to the prospect of closing the base or restrictions on its use.
The base is located on Ukraine's sensitive Crimea Peninsula, home to a large ethnic Russian population with pro-Moscow sympathies as well as some other ethnic groups.