The pilot was shot down in 1987 and is likely now to be in his 60s, according to Vyacheslav Kalinin, deputy head of a Russian veterans’ organisation.
Mr Kalinin said the pilot could be in Pakistan, where Afghanistan had camps for prisoners of war.
Valery Vostrotin, head of the Russian paratroopers’ union, told state media: “He is still alive. It’s very astonishing. Now he needs help.”
The pilot has not been named for reasons of confidentiality.
During the course of the conflict between 1979 and 1989, 125 Soviet planes were shot down in Afghanistan, according to RIA Novosti news agency.
When Soviet troops pulled out of the country in 1989, around 300 soldiers were listed as missing and since then some 30 have been found and most returned to their home countries.
Russian newspaper Kommersant reports that just one Soviet pilot was shot down in 1987, naming him as Sergei Pantelyuk, from the Rostov region in southern Russia.
He went missing along with his plane after taking off from Bagram airfield, now a US air base, north of Kabul.
The head of a local veterans’ organisation said Mr Pantelyuk’s mother and sister are both still alive.
The Komsomolskaya Pravda newspaper also traced Mr Pantelyuk’s 31-year-old daughter, who was born just months before her father went missing.
Retired colonel Frants Klintsevich told RIA Novosti that the discovery of the pilot is not the only such case, adding that he had met an ex-Soviet soldier during a trip to Afghanistan a few years ago.
Mr Klintsevich claimed the soldier refused to give his name, spoke Russian with difficulty and said it was too late for him to return.
In 2013, it was revealed that a former Red Army conscript who disappeared on the battlefield in 1980 was still alive and well in Afghanistan.
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Bakhretdin Khakimov was presumed dead by his superiors after being seriously wounded, but was nursed back to health by locals near Herat before converting to Islam.
“I stayed in Afghanistan because Afghans are very kind and hospitable people,” he told the AFP news agency.