The discovery was made after police responded to a second alert this week at the premises, with an earlier threat on Monday night later deemed a hoax.
Naomi Long MP said: “This incident is yet another senseless attack on the whole community, with the business and residential life of the local area again subjected to unnecessary disruption.
“While we are still gathering all the information around this latest discovery, I would ask anyone with information to contact the PSNI immediately.
“This is the second threat we have received in East Belfast this week, but the message is clear – those who continue to engage in bully-style tactics to target the Alliance Party will never deter us from delivering the shared future everyone in East Belfast deserves.”