The incident prompted strong criticism from Seoul, while Moscow denied that any violation had occurred.
It occurred near the islets of Dokdo off South Korea's eastern coast, known in English as the Liancourt Rocks; they are also claimed by Japan, which calls them Takeshima.
This would be the first time that a Russian aircraft has violated South Korean airspace.
Relations between the two countries have been otherwise good, with South Korea's trade minister having announced the start of bilateral trade talks in June.
The South Korean air force scrambled several fighter jets in response to the alleged violation, according to officials.
The Russian plane turned around initially but later returned for a short time, officials said.
The South Korean jets fired warning shots - 80 in response to the first encounter, then 280 the second time - as well as flares at the A-50 aircraft, officials said.
Earlier Tuesday, South Korean military officials said a number of Russian and Chinese bombers and aircraft had entered South Korea's so-called air defence identification zone (KADIZ) without giving prior notice.
It remains unclear whether the Russian and Chinese aircraft had been participating in a joint exercise.
South Korean F-16 jets "conducted unprofessional manoeuvres, crossing the course of the Russian aircraft and jeopardizing their safety," said a statement from the Russian Defence Ministry, carried by the TASS news agency.
The ministry claimed that the jets' pilots "did not establish communications" with Tu-95MS strategic bombers, which had been flying "over the neutral waters of the Sea of Japan."
Russia, however, has not responded to the allegations regarding the A-50 aircraft.
South Korean national security adviser Chung Eui Yong warned Moscow of serious consequences if there were any further violations of his country's airspace.
"We take a very grave view of this situation and, if it is repeated, we will take even stronger action," he wrote in a complaint lodged to Nikolai Patrushev, secretary of the Security Council of Russia.
South Korea also summoned Russia's acting Deputy Chief of Mission Maxim Volkov and Chinese Ambassador Qiu Guohong in protest.
The incident also angered Japan, with a government spokesman claiming that the Russian aircraft had violated his country's airspace twice near Takeshima, as that country refers to the islets.
Tokyo has "lodged a stern protest" with Moscow and Seoul over the incident near Japan's territory, Yoshihide Suga said.
South Korea announced in 2013 that it was extending the KADIZ zone to the south amid a territorial spat in the East China Sea. This area no longer belongs to South Korea, although Seoul still expects foreign aircraft to identify themselves before entering the airspace there.
South Korea says China and Russia repeatedly violate the KADIZ.
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