They said hundreds of houses burned in a fire triggered by the bombing.
The attack occurred on Wednesday in Kyauk Ni Maw village on Ramree island, an area controlled by the ethnic Arakan Army in western Rakhine state, they said.
The military has not announced any attack in the area.
The situation in the village could not be independently confirmed, with access to the internet and mobile phone service in the area mostly cut off.
Myanmar is wracked by violence that began when the army ousted the elected government of Aung San Suu Kyi in February 2021.
After the army used lethal force to suppress peaceful demonstrations, many opponents of military rule took up arms and large parts of the country are now embroiled in conflict.
A fire started by an army air strike destroyed more than 500 houses, a local group says. (AP PHOTO)
Khaing Thukha, a spokesman for the Arakan Army, told the Associated Press that a jet fighter bombed the village on Wednesday afternoon, killing 40 civilians and injuring more than 20 others.
"All the dead were civilians. Among the dead and injured are women and children," he said.
A fire started by the air strike spread through the village, destroying more than 500 houses, Khaing Thukha added.
It was unclear why the village was targeted.
The leader of a local charity group and independent media also reported the air strike and casualties.
The military government has stepped up air strikes over the past three years on armed pro-democracy groups collectively known as the People's Defence Force and on armed ethnic minority groups that have been fighting for decades for greater autonomy.
The two groups sometimes carry out joint operations against the army.
Ramree, 340km northwest of Yangon, the country's largest city, was captured by the Arakan Army in March last year.
The Arakan Army is the well-trained and well-armed military wing of the Rakhine ethnic minority movement which seeks autonomy from Myanmar's central government.
It is also a member of an alliance of armed ethnic groups that recently gained strategic territory in the country's northeast on the border with China.
It began its offensive in Rakhine in November 2023 and has gained control of a strategically important regional army headquarters and 14 of Rakhine's 17 townships, leaving only the state's capital Sittwe and two important townships near Ramree still in military government hands.
A leader of the charity group, which has been assisting residents of the village, told AP on Thursday that at least 41 people were killed and 50 others were injured in the air strike, which targeted the village's market.
The leader, who was away from the town at the time of the air strike, spoke on condition of anonymity because of security concerns.
He said he received the information from members of his group who were in the village and were facing a shortage of medicine to treat the injured people.
Rakhine-based news outlets including Arakan Princess Media also reported the attack and posted photos online showing people putting out fires at their homes.
Rakhine, formerly known as Arakan, was the site of a brutal army counterinsurgency operation in 2017 that drove about 740,000 minority Rohingya Muslims to seek safety across the border in Bangladesh.
