The flights took off from Moscow within minutes of each other Tuesday night and were bound for cities in southern Russia.
Witnesses reported seeing the first plane explode before it crashed, the Russian news agency Interfax reported.
The government-run news agency Ria Novosti reported that the plane's wreckage was in two separate locations.
The second plane, carrying with between 46 and 52 people on board, was about 100 miles (160 kilometers) from Rostov-on-Don when it dropped off radar screens.
The first plane disappeared from radar at 10:56 p.m. (0756 GMT), the news agency said.
The Tupolev-134 had taken off from Moscow's Domodedovo Airport and was en route to Volgograd, in southern Russia.
The second plane, a Tupolev-154, disappeared from radar at 10:59 p.m. after having taken off from the same airport en route to Sochi, a tourist resort on the Black Sea in southern Russia, the ministry spokeswoman reported.
The Tupolev-154 is a standard medium-range airliner on domestic flights in Russia, according to aviation websites.
Russian authorities offered no explanations for the crashes but said they had increased security at airports following an explosion at a Moscow bus station earlier Tuesday, which injured three people.
"If this were just one, you would look toward some sort of aircraft issue," Peter Goelz, a former managing director of the U.S. National Transportation Safety Board, told CNN.
"But with two of them going down so close together, it's awfully ominous."