West Belfast MP Paul Maskey said the object was left at the front gates of Connolly House on the Andersonstown Road on Monday evening.
He criticised those responsible.
Police Service of Northern Ireland spokesman said officers received a report of a suspect device at around 10.15pm.
A public safety operation was launched, and Army bomb experts examined the device before declaring it to be a hoax.
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Inspector Robert Jeffers said: “Thank you to the local community and anyone who was impacted last night as we dealt with the incident.
“I would appeal to anyone with information about this incident to call us on 101, quoting reference number 2240 of 27/07/20.”
Mr Maskey said: “This office provides an invaluable service to our community on a daily basis and has done sterling work during the Covid-19 pandemic to support the most vulnerable in our community.
“We will not be deterred by those attacking a community asset.
“Sinn Fein will continue to work to deliver for constituents and to build a just, equal and united Ireland.”
The property was previously damaged in an arson attack in August 2018.