The Syrian Observatory for Human Rights monitoring group said the pilot ejected and was killed, but this has not yet been confirmed.
Video posted on social media appeared to show the plane being hit, while other video showed burning wreckage on the ground, with a red star on a wing.
Russia has acted alongside its Syrian allies targeting rebels in the area.
Syrian government troops launched a major offensive around Idlib in late December, backed by Russian jets. The UN says some 100,000 civilians have been displaced.
The Syrian Observatory told Agence France-Presse there had been dozens of Russian air strikes in the area over the past 24 hours.
There are several reports that Russia has now fired cruise missiles into Idlib province from navy vessels in the Mediterranean.
It is not yet known which group shot the plane down. Reports say the pilot ejected and landed via parachute.
One social media video posting showed a body said to be that of the pilot but there is no independent confirmation of the airman's fate.
Hardline rebel groups including the jihadist, al-Qaeda-linked Hayat Tahrir al-Sham are active in the north-western province.
Russian air force losses have been rare since it began its Syria campaign in September 2015.
The defence ministry has not yet commented on the latest incident.
About 45 Russian military personnel have been confirmed dead in Syria, along with an unknown number of contractors.