A member of the public reported hearing a bang at 6am on Saturday.
Earlier reports had suggested that petrol was poured through the shutters of the office at Graham Gardens,
But police have now said it was caused by a “pipe-type explosive device”. There was some fire damage to the office.
The party’s Lagan Valley MLA, Trevor Lunn, condemned the attack: “This is an attack on democracy. There is no place in our society for this violence that should be condemned by all.
“This attack will not deter us from continuing to work on behalf of the people of Lagan Valley.
“This is the latest in a number of attacks on Alliance Party offices, but we will not give in to violence and intimidation. Alliance will continue to work to achieve a shared future for everyone.
“I would urge anybody with any information about this attack to contact the police.”
Justice minister and Alliance leader, David Ford, said: “It is extremely worrying. It’s not going to affect the work we do, but it’s a disappointing example of what some people are still up to and has to be condemned by everyone.”
Lagan Valley MP, Jeffrey Donaldson (DUP), said the attack was “an assault on democracy itself”.
“Whether it is bombs in Belfast or an arson attack in Lisburn, such criminal actions are designed to undermine those rights and damage democracy,” he said.
Police want to speak to anyone who was in the Bachelor’s Walk or Railway Street area between 5.30am and 6.30am on Saturday.