Kenya, Uganda and Burundi contribute most of the 17,700 soldiers in the African Union's AMISOM force battling the Shebab in Somalia.
"Since the attack in Nairobi and the subsequent rumours of an impending attack in Burundi, the police have implemented a series of measures to be ready for any scenario," Burundian deputy police spokesman Pierre Nkurikiye told AFP.
The Al Qaeda-linked Shebab claimed responsibility for the bloody four-day siege in a shopping centre packed with families, leaving at least 67 people dead, including many foreigners.
Kenyan troops have since recaptured the main southern city of Kismayo, which was controlled by the Shebab for four years, and joined the African Union's AMISOM force.
Uganda was hit in 2010 when Shebab attacks killed at least 76, Kenya was struck on Saturday and now many Burundians fear their country's turn has come.
"We are sure that after Kenya, Burundi is next on the list. We're the next target," said a civil servant in his sixties who gave his name as Patrice.
"They managed to perpetrate this attack Saturday... In a country that is much better prepared for terrorist attacks," said Alain, a Bujumbura banker. "In Bujumbura's official buildings, hospitals and markets, security is like Swiss cheese."
The police spokesman said house-to-house searches had been being carried out in the Swahili neighbourhoods of Bujumbura, with hundreds of undocumented people arrested and drugs and weapons seized.
Shebab has repeatedly threatened reprisal attacks against Burundi, which has no borders with Somalia.
Uganda also said today that it raised the alert level in response to the Westgate mall attack.
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