The photo has been used for illustrative purposes.
The inquiry comes as around a million Rohingya in vast camps in Bangladesh face increasing hostility two years after fleeing a military offensive in Myanmar.
Mohammad Osman, an elder brother of the alleged victim, said three soldiers entered their shanty at the Nayapara Rohingya camp on Sunday evening and sexually assaulted his sister.
"She was raped as one of them tightly held her mouth," he told AFP by phone, referring to the border district where the refugee camps are located.
A spokesman of the Bangladesh Armed Forces, Lieutenant Colonel Abdullah ibn Zaid, said they were investigating.
"We have formed a probe committee to investigate the incident and find out the facts. If (they are) found guilty, exemplary punishment will be given," Ibn Zaid said.
Doctor Shaheen Abdur Rahman said the girl was examined at the central hospital in Cox's Bazar but he refused to comment on the findings due to court restrictions.
A spokesman of the United Nations High Commissioner for Refugees said they were also investigating the incident.
"We are aware of the reports. In such cases, individuals are entitled to medical, physical and psychological support, as well as access to due process," UNHCR spokesman Joseph Tripura said in a statement to AFP.
Tensions have risen in recent weeks with an increasingly frustrated Bangladeshi government enacting several measures making life harder for the refugees.
These include blocking mobile internet, confiscating SIM cards and mobile phones and filing hundreds of cases for illegally obtaining citizenship cards.
UN experts have expressed "serious concerns" about the restrictions.
Last week Bangladesh's home minister said that barbed-wire fencing, guard towers and cameras would be erected around the Rohingya camps, sparking criticism from rights groups.
Checkpoints set up on the main highways leading to the camps have stopped Rohingya and sent them back to the settlements when they try to travel to other parts of Bangladesh.
Hundreds of Rohingya found elsewhere in the South Asian nation have also been detained and returned to the camps.
Authorities say the internet ban was sparked by security fears after the Rohingya were blamed for the murder of a local politician and drug smuggling.
A total of 582 Rohingya escaped the Sungai Bakap temporary immigration detention camp in northern Penang state by breaking down doors and barrier grills, though 362 have since been re-arrested, the immigration department said in a statement.
The exodus of Rohingya was sparked by a 2017 Myanmar army offensive against the mostly Muslim minority, with the UN's highest court last month giving the green light to a landmark case accusing the Buddhist-majority country of genocide.
If there is one breed of people whose position shows no sign of improvement, it is the refugees. Be it in Bangladesh or Lebanon, their predicament seems precarious as they get tossed around from place to place – homeless, hapless, helpless.
Sheikh Mohamed Bin Zayed Al Nahyan, Sheikhs and guests of the country witnessed on Sunday the “Union March”, which was organised by the Presidential Office and launched as part of the activities of the Sheikh Zayed Heritage Festival for 2023 in Al Wathba area in Abu Dhabi.
At least 26 people were injured — including a local cleric — and transferred to hospitals. Police helped reroute traffic in the area after condoning off the site, officials said. The interior minister of Gilgit-Baltistan called the incident an "act of terrorism.”
Modi thanked voters for "their unwavering support” in the states where his party was leading. Rahul Gandhi, the Congress leader, conceded defeat in the three states where his party was trailing.