Nobel peace laureate Malala Yousafzai and Muslim countries in Asia led a growing chorus of criticism on Monday aimed at Myanmar and its civilian leader Aung San Suu Kyi over the plight of its Rohingya Muslim minority.

Nearly 90,000 Rohingya have flooded into Bangladesh in the past 10 days following an uptick in fighting between militants and Myanmar's military in strife-torn western Rakhine state.

The impoverished region bordering Bangladesh has been a crucible of communal tensions between Muslims and Buddhists for years, with the Rohingya forced to live under apartheid-like restrictions on movement and citizenship.

The recent violence, which kicked off last October when a small Rohingya militant group ambushed border posts, is the worst Rakhine has witnessed in years with the UN saying Myanmar's army may have committed ethnic cleansing in its response.

De facto leader Suu Kyi, a former political prisoner of Myanmar's junta, has come under increasing fire over her perceived unwillingness to speak out against the treatment of the Rohingya or chastise the military.

She has made no public comment since the latest fighting broke out.

"Every time I see the news, my heart breaks at the suffering of the Rohingya Muslims in Myanmar," Pakistani activist Yousafzai, who famously survived being shot in the head by the Taliban, said in a statement on Twitter.

"Over the last several years I have repeatedly condemned this tragic and shameful treatment. I am still waiting for my fellow Nobel laureate Aung San Suu Kyi to do the same," she added.

Muslim neighbours riled

The growing crisis threatens Myanmar's diplomatic relations, particularly with Muslim-majority countries in Southeast Asia where there is profound public anger over the treatment of the Rohingya.

The Maldives announced on Monday that it was severing all trade ties with the country "until the government of Myanmar takes measures to prevent the atrocities being committed against Rohingya Muslims", the foreign ministry said in a statement.

It did not say say how much trade took place between the two countries but it could prompt other Muslim nations to follow suit.

Indonesia's foreign minister Retno Marsudi met Suu Kyi as well as Myanmar's army chief General Min Aung Hlaing in Naypyidaw on Monday in a bid to pressure the government to do more to alleviate the crisis.

"Once again, violence, this humanitarian crisis has to stop immediately,"  Indonesian president Joko Widodo told reporters on Sunday as he announced Retno's mission.

Hours before Widodo spoke, a petrol bomb was thrown at Myanmar's embassy in Jakarta while police there have previously dismantled two attempts by Islamist militants to bomb the compound.

Dozens demonstrated in front of the embassy on Monday, where armed police were deployed and the mission cordoned off behind barbed wire.

Pakistan's foreign ministry said it was "deeply concerned over reports of growing number of deaths and forced displacement of Rohingya Muslims" and urged Myanmar to investigate reports of atrocities against the community.

Iranian foreign minister Javad Zarif added in a recent tweet: "Global silence on continuing violence against #Rohingya Muslims. Int'l action crucial to prevent further ethnic cleansing - UN must rally."

Muslim-majority Malaysia has also seen public protests since the latest round of violence began.

"We urge for calm and restraint," Prime Minister Najib Razak tweeted. "The dire situation facing our Rohingya brothers and sisters must be alleviated for good of Myanmar and region."

Analysts have long warned that Myanmar's treatment of the Rohingya would lead to homegrown militancy as well as support from international jihadists.

Since the latest fighting broke out, Al-Qaeda's offshoot in Yemen has called for retaliatory attacks against Myanmar while the Afghan Taliban called on Muslims to "use their abilities to help Myanmar's oppressed Muslims".

Defenders of Suu Kyi say she is limited in her ability to control Myanmar's notoriously abusive military, which under Myanmar's junta-era constitution is effectively independent of any civilian oversight.

The Rohingya are also widely dismissed in Myanmar as Bangladeshi interlopers despite many tracing their lineage back generations, making supporting them hugely unpopular.

But detractors say Suu Kyi is one of the few people with the mass appeal and moral authority to swim against the tide on the issue. (AFP)