According to Twitter users are blocked "for any unlawful purposes or in furtherance of illegal activities".
The Shabab's previous account, @HSMPress, was suspended in January after the group posted photographs of a French commando they killed and threatened to execute Kenyan hostages. They opened another account, @HSMPress1, but were again suspended earlier this month after threatening Somalia's internationally-backed president.
The group issued a string of messages on Twitter Saturday, claiming its fighters were behind an attack on Nairobi's upmarket Westgate shopping mall.
"The Mujahideen entered #Westgate Mall today at around noon and are still inside the mall, fighting the #Kenyan Kuffar (infidels) inside their own turf," the Islamist militants had said on Twitter.
"What Kenyans are witnessing at #Westgate is retributive justice for crimes committed by their military," the group said.