Rohingya Muslims fleeing unrest in Myanmar have been injured by multiple blasts along the border with Bangladesh, raising fears that the area has been deliberately mined.

Two Rohingya children were injured in an apparent landmine blast on Tuesday as they tried to flee Myanmar with one losing a leg, according to a Bangladesh border official.

The incident came after a Rohingya woman had her leg blown off in the same area on Monday.

"They stepped onto some sort of explosives this morning and one of them lost his leg," border guard commander Manzurul Hasan Khan told AFP on Tuesday of the two children.

It is not known what caused the blast, which he said was well inside Myanmar territory, but Khan said he believed it was a landmine.

Khan said a Rohingya woman had been brought to the border on Monday after losing half her leg in a blast, hours after guards heard a loud explosion from the Myanmar side.

Many Rohingya were also entering Bangladesh with bullet wounds, although it was impossible to say how these were sustained as media access to the worst-hit parts of Myanmar's neighbouring Rakhine state is limited.

All three have been taken to hospitals in Cox's Bazar, the nearest city to the border, where hundreds of thousands of Rohingya - a stateless Muslim minority in mainly Buddhist Myanmar - have taken shelter in camps.

Nearly 125,000 Rohingya Muslim refugees have fled to Bangladesh since an upsurge in violence on 25 August, the United Nations said on Tuesday.

At least 37,000 have arrived in the last 24 hours, the highest number in a single day since the unrest began.

The Rohingya are seen as illegal immigrants in Myanmar and have suffered decades of persecution, according to rights groups.

Unverifiable testimony from those who have fled indicates tit-for-tat mass killings and villages being torched by the army, Buddhist mobs and Rohingya militants.

In addition to the Rohingya at least 11,000 Rakhine Buddhists and Hindus have fled arson and attacks by militants to camps inside Myanmar, according to the last government update.