Thousands of demonstrators stormed her official residence on Monday, a day after nearly 100 died in the unrest.
Prime Minister Sheikh Hasina's departure threatens to create even more instability in the nation on India's border already dealing with crises including high unemployment, corruption and climate change.
Hours after the embattled leader boarded a military helicopter with her sister, the country's military chief, General Waker-uz-Zaman, said he would seek the president's guidance on forming an interim government.
He promised the military would launch an investigation into the deadly crackdown on student-led protests that fuelled outrage against the government.
Sheikh Hasina was re-elected in a January vote that was boycotted by her main opponents. (AP PHOTO)
"Keep faith in the military, we will investigate all the killings and punish the responsible," he said.
"I have ordered that no army and police will indulge in any kind of firing."
He met opposition politicians, including the head of the now-banned Jamaat-e-Islami party, and civil society members before making his statement.
The protests began peacefully as frustrated students demanded an end to a quota system for government jobs they said favoured those with connections to the prime minister's Awami League party, but the demonstrations morphed into an unprecedented challenge to Hasina and the party.
The 76-year-old - who was the longest-serving female head of government - was elected for a fourth consecutive term in a January vote that was boycotted by her main opponents.
Thousands of opposition members were jailed in the lead-up to the polls, and the US and the UK denounced the result as not credible, though the government defended it.
The protests began peacefully about job quotas but morphed into an anti-government uprising. (AP PHOTO)
Hasina had cultivated ties with powerful countries, including India and China.
But under her, relations with United States and other Western nations have come under strain as they have expressed concerns over human rights violations and press freedoms in the predominantly Muslim nation of 170 million people.
Her political opponents have accused her of growing increasingly autocratic, and many say the unrest is a result of that authoritarian streak.
Hasina arrived on Monday in a city in India on the border with Bangladesh in an army helicopter, according to a military official who spoke on condition of anonymity, but it was not clear where she would go next.
As she fled, people stormed her residence, taking furniture and pulling food from the refrigerators.
Protests have continued even after the Supreme Court in July ruled the quota system - which set aside up to 30 per cent of government jobs for family members of veterans who fought in Bangladesh's war of independence against Pakistan - must be drastically cut.
Prime Minister Sheikh Hasina railed against protesters who engaged in "sabotage". (AP PHOTO)
The government attempted to quell the demonstrations with force, leaving nearly 300 people dead since mid-July.
At least 95 people, including at least 14 police officers, died in clashes in the capital on Sunday, according to the country's leading Bengali-language daily newspaper, Prothom Alo.
Hundreds more were injured.
At least 11,000 people have been arrested in recent weeks.
The unrest has also resulted in the closure of schools and universities across the country, and authorities at one point imposed a shoot-on-sight curfew.
Authorities also shut off mobile internet on Sunday, and broadband internet was cut briefly on Monday morning.
The unrest resulted in Bangladesh authorities at one point imposing a shoot-on-sight curfew. (AP PHOTO)
It was the second internet blackout in the country since July.
Protesters called for a "non-co-operation" effort, urging people not to pay taxes or utility bills and not to show up for work on Sunday.
Hasina offered to talk with student leaders on Saturday but a co-ordinator refused and demanded her resignation.
Hasina repeated her pledges to investigate the deaths and punish those responsible for the violence.
She said she was ready to sit down whenever the protesters wanted.
Earlier, she had said protesters who engaged in "sabotage" and destruction were no longer students but criminals, and the people should deal with them with an iron hand.
