"As per recommendation from the home ministry, we have given directives to all the telecoms service providers to unblock Facebook immediately," telecommunication minister Tarana Halim said.
However, the bans on WhatsApp and Viber would continue for "security reasons", Halim said as he thanked people for "keeping patience" during the ban.
Facebook, WhatsApp and Viber were blocked last month after the death penalty was upheld by the Supreme Court.
The social networking sites were blocked as the government feared they could be used to mobilise anti-government protests.
Similar convictions of opposition leaders in 2013 had sparked country's deadliest violence since independence, with over 500 people killed in clashes between the security forces and opposition activists.
The government had also blocked Facebook during a paramilitary revolt in 2009 that left over 50 army officers dead and video-sharing website YouTube for 260 days between September 2012 and June 2013.