Russia was blamed by Syrian opposition activists for the attacks, which left at least 44 people dead on Sunday.
IHH said via Twitter on Monday that the bakery, which was established 16 months ago, provided daily bread for nearly 45,000 internally displaced Syrians.
Mustafa Ozbek, from IHH’s media office, told Reporters that the bakery is in the town of Saraqeb and was destroyed in the attack.
“They completely destroyed our bakery and flour mill which was in the building. This bakery was very important because it provided bread for internally displaced Syrians.
“Locals said the air strikes were launched by Russian jets, adding that Russians have been targeting those areas in the past few days,” Ozbek said.
“At least 20 missiles were dropped by four Russian warplanes, they said”
“It is the first time any of our facilities are targeted, but activists said trucks loaded with humanitarian aid and food storages have been targeted too.”
None of the employees were killed in the attack, IHH said.
The air strikes also targeted a crowded marketplace and several other areas in Idlib province.
Bulent Yildirim, IHH’s president, told Turkish Anadolu news agency: “If bakeries, camps are attacked, that means the aim is to eliminate all Syrian people.”
IHH officials told Turkey’s Daily Sabah that the Russian warplanes first targeted positions close to the bakery as a warning, but as the people in the bakery left, the jets struck again and demolished the building.
The Russian government has yet to respond to IHH’s accusations.
Tensions grew between the two countries after Turkey shot down a Russian fighter jet which it says violated its airspace and was warned repeatedly.
Elsewhere in Syria, the UK-based Syrian Observatory for Human Rights said that at least five people were killed, including one child, in suspected Russian air strikes.
The raids targeted the town of Azaz in Aleppo province on Sunday evening, the activists’ network said.
Syria’s Civil Defence, a team of civilian rescue workers, said seven trucks loaded with humanitarian aid were also targeted in the air strikes.
Russia says it targets the Islamic State of Iraq and the Levant (ISIL) group and other “terrorists”, but critics accuse it of targeting other rebel groups more than ISIL.
Idlib is not a stronghold of ISIL, which controls wide areas of eastern Syria.
The Syrian Observatory reported last week that Russian air operations have killed over 400 civilians since Russian forces launched their first air strike in September this year.
The Syrian conflict has killed at least 250,000 people, according to the UN, and more than half of Syria’s prewar population of 22.4 million has been internally displaced or have fled abroad.