"Effective July 10, 2016, the Department of State authorized the voluntary departure of family members of US government personnel posted to the US Embassy in Dhaka," the release stated.
The State Department underscored that the terrorist threat in Bangladesh is "real and credible."
"The US Embassy in Dhaka remains open and will provide all routine consular services,” the warning added.
On Thursday, at least 12 people were injured and one policeman killed in an explosion at Eid celebration in Bangladesh, which marks the end of the Islamic holy month Ramadan.
The attack came after the July 1 assault, when a group of armed terrorists took dozens hostage inside the restaurant located in a diplomatic quarter of the Bangladeshi capital Dhaka. The attack left 20 people, mostly foreigners, dead, while 13 hostages were rescued by the country's security forces.