Al-Shabaab used the account Thursday to say it would kill a group of hostages if Kenya does not free militants detained on terrorism charges, Voice of America reported.
In Twitter messages, the militants said the six hostages shown on a video would be executed if the Kenyan government does not respond by Feb. 14.
The group's Arabic-language Twitter account, which was not shut down, confirmed the suspension.
Kenya did not immediately respond to the Twitter demand, but a spokesman for the Defense Ministry said it was aware of two Kenyan civil servants being held by the group.
"We do not want to negotiate with terrorists," Kenyan Prime Minister Raila Odinga said at the World Economic Forum in Davos, Switzerland.
"We expect them to surrender Kenyan citizens who they are holding hostage without any kind of conditions whatsoever," he added.
CNN reported Odinga called terrorism an "international affair" that required a global response.
Kenya has been a target of al-Shabaab attacks since Kenyan military forces intervened in Somalia in October 2011.
Last week, al-Shabaab tweeted graphic images of the body of a French hostage who died during an unsuccessful raid by French forces to free him.