The announcement by the state department prohibits US citizens to engage in transactions with AQIS and Umar and the freezing of all of their property and interests in the US.
In addition, the consequences of AQIS' FTO designation include a prohibition against knowingly providing, or attempting or conspiring to provide, material support or resources to the organization.
In a video message in September 2014, Al Qaeda leader Ayman al-Zawahiri had announced the formation of AQIS to take the fight to India, Myanmar and Bangladesh.
The group is led by Umar, a former member of US designated Foreign Terrorist Organisation Harakat ul-Mujahidin.
AQIS claimed responsibility for the September 6, 2014 attack on a naval dockyard in Karachi, in which militants attempted to hijack a Pakistani Navy frigate.
It has also claimed responsibility for the murders of activists and writers in Bangladesh, including that of US citizen Avijit Roy, US Embassy local employee Xulhaz Mannan, and of Bangladeshi nationals Oyasiqur Rahman Babu, Ahmed Rajib Haideer and AKM Shafiul Islam.
"This action notifies the US public and the international community that AQIS and Umar are actively engaged in terrorism," the state department said.
"Designations of terrorist individuals and groups expose and isolate organizations and individuals, and result in denial of access to the US financial system. Moreover, designations can assist or complement the law enforcement actions of other US agencies and other governments," it said.