Twitter did not give any reasons for the suspension of the account, the New York Daily News reported.
Using the handle, the terrorist organisation began posting tweets in Arabic. The account gained more than 1,500 followers.
But on Sunday, when users clicked on the profile, the social media website indicated that the account had been suspended. The suspension followed criticism in the media.
In the "Twitter Rules" section for the site, the company says an account can be shut down if it is being used to propagate "violence and threats" or is "in the furtherance of illegal activities."
The State department declined to confirm the validity of the account or say whether US officials suspect it is real.
The account, sent out 47 tweets since its launch. Most recently, the account appeared to justify terrorism.
Last week, a representative for the Somalia-based terror organisation Al Shabab also set up a Twitter account, but that was also quickly shut down.