"Unfortunately it was not possible to resuscitate the pilot," an Aeroflot spokesman told RBC news.
"He died in the ambulance. We express our sincere condolences to his family and friends."
A female passenger told the Mirror: "A female flight attendant ran through the plane asking if there was a doctor because one of the crew members was feeling unwell.
"Several minutes later we were told that the aircraft was performing an emergency landing."
A source told Russian News agency TASS that the pilot "died during the landing".
Flight SU1546 was flying from Moscow at 8.20am (local time) to the resort town of Anapa on the Black Sea with the scheduled time of 10.40am, but instead landed at Rostov at 9.57am.
It has been reported that the passengers were able to continue to Anapa with a replacement co-pilot.
The Russian Investigative Committee's southern investigative department has launched a probe into the pilot's death.